Updated Answer
My original answer below has some good stuff so I left it below my new answer but I discovered later that it has a fatal flaw. Peter is not providing a theodicy for the delay of the arrival of triumphant Israel but rather for the delay of judgment on earthly, old covenant Israel!
First of all, it is important to realize that for the new covenant Jews, the old covenant Jews were a mortal enemy. They were persecuting the apostles and the believers in the Messiah. The new covenant saints pined for the day of judgment like men at sea search the horizon for morning light:
[Rev 6:10 KJV] (10) And they cried with a loud voice, saying, How long, O Lord, holy and true, dost thou not judge and avenge our blood on them that dwell on the earth?
[2Th 1:4-10 KJV] (4) So that we ourselves glory in you in the churches of God for your patience and faith in all your persecutions and tribulations that ye endure: (5) Which is a manifest token of the righteous judgment of God, that ye may be counted worthy of the kingdom of God, for which ye also suffer: (6) Seeing it is a righteous thing with God to recompense tribulation to them that trouble you; (7) And to you who are troubled rest with us, when the Lord Jesus shall be revealed from heaven with his mighty angels, (8) In flaming fire taking vengeance on them that know not God, and that obey not the gospel of our Lord Jesus Christ: (9) Who shall be punished with everlasting destruction from the presence of the Lord, and from the glory of his power; (10) When he shall come to be glorified in his saints, and to be admired in all them that believe (because our testimony among you was believed ) in that day.
The promise Jesus made about his return to snatch up the saints is not what has delayed and is causing concern. It is the fact that the promise that God made to Israel in Deuteronomy 32, to punish them "soon" seems to have been forgotten about:
[Deu 32:35-36 HNV] (35) Vengeance is mine, and recompense, At the time when their foot shall slide: For the day of their calamity is at hand, The things that are to come on them shall make haste. (36) For the LORD will judge his people, Repent himself for his servants; When he sees that their power is gone, There is none remaining, shut up or left at large.
So it is in reference to God's promise to the fathers that Peter is speaking:
[2Pe 3:4 ESV] (4) They will say, "Where is the promise of his coming? For ever since the fathers fell asleep, all things are continuing as they were from the beginning of creation."
Peter seems to be responding to the argument that God promised never to destroy the world again:
[Gen 9:15 KJV] (15) And I will remember my covenant, which is between me and you and every living creature of all flesh; and the waters shall no more become a flood to destroy all flesh.
Peter seems to be saying that God decided that rather than have regular cycles of sin then deluge, sin then deluge that he would never again flood the earth as he did and would save it up for a single judgment at the end.
[Deu 32:33-36 HNV] (33) Their wine is the poison of serpents, The cruel venom of asps. (34) Isn't this laid up in store with me, Sealed up among my treasures? (35) Vengeance is mine, and recompense, At the time when their foot shall slide: For the day of their calamity is at hand, The things that are to come on them shall make haste. (36) For the LORD will judge his people, Repent himself for his servants; When he sees that their power is gone, There is none remaining, shut up or left at large.
Notice that Peter says that wrath is "stored up" for the current "heavens and the earth" - referring to the temple in Jerusalem!:
[2Pe 3:4, 7 NLT] (4) They will say, "What happened to the promise that Jesus is coming again? From before the times of our ancestors, everything has remained the same since the world was first created." ... (7) And by the same word, the present heavens and earth have been stored up for fire. They are being kept for the day of judgment, when ungodly people will be destroyed.
Peter compares the destruction of the first "heaven and earth" by water with the destruction of the "current heaven and earth", referring to the temple. The bottom line of his argument is that the original promise in Deuteronomy, that God would judge the current temple, his people, Jerusalem, the old covenant, etc. will be fulfilled, by fire. And this of course is exactly what happened in 70ad.
And yes, this happened at the second coming of Christ circa 70ad.
Original Answer
1 & 2 Peter are Jewish scrolls intended for a Jewish audience about Jewish concerns. Peter and the other apostles (except Paul) were trained by the earthly Jesus concerning the kingdom of God (triumphant, eschatological Israel). Peter's expectation was that Jesus would judge temple-centric Judaism, humiliate the nations and rule from Jerusalem as the descendant of David:
NIV Acts 1:6 Then they gathered around him and asked him, “Lord, are
you at this time going to restore the kingdom to Israel?”
However, the triumph of Israel was still thousands of years off because the Jewish leadership rejected their messiah. Instead Paul was sent to the gentiles:
NIV Acts 13:46 Then Paul and Barnabas answered them boldly: "We had to
speak the word of God to you first. Since you reject it and do not
consider yourselves worthy of eternal life, we now turn to the
Gentiles.
This is what Jesus warned would happen:
ESV Matthew 21:
33“Hear another parable. There was a master of a house who planted a
vineyard and put a fence around it and dug a winepress in it and built
a tower and leased it to tenants, and went into another country.
34When the season for fruit drew near, he sent his servantsc to the
tenants to get his fruit. 35And the tenants took his servants and beat
one, killed another, and stoned another. 36Again he sent other
servants, more than the first. And they did the same to them.
37Finally he sent his son to them, saying, ‘They will respect my son.’
38But when the tenants saw the son, they said to themselves, ‘This is
the heir. Come, let us kill him and have his inheritance.’ 39And they
took him and threw him out of the vineyard and killed him. 40When
therefore the owner of the vineyard comes, what will he do to those
tenants?” 41They said to him, “He will put those wretches to a
miserable death and let out the vineyard to other tenants who will
give him the fruits in their seasons.”
42Jesus said to them, “Have you never read in the Scriptures:
“‘The stone that the builders rejected has become the cornerstone;d
this was the Lord’s doing, and it is marvelous in our eyes’?
43Therefore I tell you, the kingdom of God will be taken away from you
and given to a people producing its fruits. 44And the one who falls on
this stone will be broken to pieces; and when it falls on anyone, it
will crush him.”e
45When the chief priests and the Pharisees heard his parables, they
perceived that he was speaking about them. 46And although they were
seeking to arrest him, they feared the crowds, because they held him
to be a prophet.
Peter's letters are written to faithful Jews who looked for the arrival of the kingdom. However, it appears Peter had to reconcile himself to the fact that due to disobedience the arrival of the kingdom would be delayed for thousands of years:
NIV 2 Peter 3:
8But do not forget this one thing, dear friends: With the Lord a day
is like a thousand years, and a thousand years are like a day. 9The
Lord is not slow in keeping his promise, as some understand slowness.
Instead he is patient with you, not wanting anyone to perish, but
everyone to come to repentance.
Note that Peter's gospel of the kingdom (which he got from the earthly Jesus) is definitely not "faith without works". One must watch and pray, laboring to be found as a torah observant Jew:
NIV 1 Peter 4:17:For the time is come that judgment must begin at the
house of God: and if it first begin at us, what shall the end be of
them that obey not the gospel of God? 18: And if the righteous
scarcely be saved, where shall the ungodly and the sinner appear?
ESV 2 Peter 1:
10Therefore, brothers,g be all the more diligent to confirm your
calling and election, for if you practice these qualities you will
never fall. 11For in this way there will be richly provided for you an
entrance into the eternal kingdom of our Lord and Savior Jesus Christ.
This is in sharp contrast to Paul's gospel where the believer is immediately "translated" into Christ's kingdom:
ESV Colossians 1:
12 ...giving thanks to the Father [IE: God], who has qualified you
to share in the inheritance of the saints in light [NOT Israel]. 13 He
[God] has delivered us from the domain of darkness and [has]
transferred us to the kingdom of his beloved Son, 14 in whom we have
redemption, the forgiveness of sins.
Peter and the Jewish community are living in the last days of the Jewish temple-centric theocracy. During the last days of the theocracy God's spirit was poured out on Jews and gentiles alike, male and female to wait for Jesus to descend from the sky and overthrow Rome.
NIV Acts 2:17“ ‘In the last days [of temple-centric Judaism], God
says, I will pour out my Spirit on all people. Your sons and daughters
will prophesy, your young men will see visions, your old men will
dream dreams. 18Even on my servants, both men and women, I will pour
out my Spirit in those days, and they will prophesy.
This outpouring of the spirit (the "baptism in the spirit") gave to the Jews of that time all they needed to live godly lives in preparation to meet the king:
NIV 2 Peter 3:
3His divine power has given us everything we need for a godly life
through our knowledge of him who called us by his own glory and
goodness. 4Through these he has given us his very great and precious
promises, so that through them you may participate in the divine
nature, having escaped the corruption in the world caused by evil
desires.
However, the kingdom was forfeited because the leaders rejected the messiah. So they Jews gathered in Jerusalem, sold all they had and the like but Jesus did not show. Instead the stumbling stone fell upon the heads of the Jewish leaders, the Jews in Israel became poverty stricken and Rome crushed the Jewish rebellion. After 70AD the Jewish believers hopefully were subsumed into the new humanity and gospel of the grace of God that the risen Christ sent to Paul to dispense.
So what about the 1000 year reign? The 1000 year reign is a period of time where Christ rules from Jerusalem over the entire world specifically for the purpose of demoralizing the gentiles into submission to God. Once all of God's enemies are securely underfoot Jesus will become the subject king of Israel only so that God may be all in all:
NIV 1 Cor 15:
24Then the end will come, when he hands over the kingdom to God
the Father after he has destroyed all dominion, authority and power.
25For he must reign until he has put all his enemies under his feet.
26The last enemy to be destroyed is death. 27For he “has put
everything under his feet.” Now when it says that “everything” has
been put under him, it is clear that this does not include God
himself, who put everything under Christ. 28When he has done this,
then the Son himself will be made subject to him who put everything
under him, so that God may be all in all.
This matter of the temporary nature of the 1000 year reign is extremely important and overlooked by most:
NIV Matthew 22:44 The LORD said to my Lord, Sit in the place of honor
at my right hand until I humble your enemies beneath your feet.'
However, this humiliation of the nations was not to occur immediately because the dramatic rescue of Zechariah 14 was postponed:
NIV Zechariah 14:
1A day of the Lord is coming, Jerusalem, when your possessions will be
plundered and divided up within your very walls.
2I will gather all the nations to Jerusalem to fight against it; the
city will be captured, the houses ransacked, and the women raped. Half
of the city will go into exile, but the rest of the people will not be
taken from the city. 3Then the Lord will go out and fight against
those nations, as he fights on a day of battle. 4On that day his feet
will stand on the Mount of Olives, east of Jerusalem, and the Mount of
Olives will be split in two from east to west, forming a great valley,
with half of the mountain moving north and half moving south. 5You
will flee by my mountain valley, for it will extend to Azel. You will
flee as you fled from the earthquake in the days of Uzziah king of
Judah. Then the Lord my God will come, and all the holy ones with him.
So to make a long story short, Peter's expectation of Jesus at this time restoring the kingdom to Israel was dashed. Or rather, deferred for thousands of years and with it the 1000 years of subjugation of the nations. Peter was concerned with the millennium, that period of subjugation of the nations under Israel but did not call it such.