Peace with God bringing Peace within Self
Ideas one and three are both present in the context. Peace with God will bring the inner peace, which is the primary focus of the word here. Expand the context to see how this works in 2 Peter 3 (ESV):
9 The Lord is not slow to fulfill his promise as some count slowness,
but is patient toward you, not wishing that any should perish,
but that all should reach repentance.
Verse 7 revealed a coming "judgment and destruction of the ungodly," that the "beloved" (v.8) were to count on would come in God's good time (v.8). But v.9 reveals God is slow in bringing it because there are "beloved" that still need to "reach repentance" else they would perish, because—
10 But the day of the Lord will come like a thief,
and then the heavens will pass away with a roar,
and the heavenly bodies will be burned up and dissolved,
and the earth and the works that are done on it will be exposed.
If ever there was news that should not bring inner peace, it is the news of such cosmic cataclysm and the exposing of people's works in this coming "day of the Lord."
11 Since all these things are thus to be dissolved,
what sort of people ought you to be in lives of holiness and godliness,
Because of this coming judgment, there is an obvious conclusion that one ought to be holy and godly (from εὐσέβεια, i.e. devout or pious toward God).
12 waiting for and hastening the coming of the day of God,
because of which the heavens will be set on fire and dissolved,
and the heavenly bodies will melt as they burn!
More news to give one warm and tingly feelings (pun intended), but the incredible thing is the fact that the beloved are to be "waiting" for it, and even "hastening" it to come. This is because—
13 But according to his promise we are waiting for new heavens
and a new earth in which righteousness dwells.
14 Therefore, beloved, since you are waiting for these,
be diligent to be found by him without spot or blemish, and at peace.
15 And count the patience of our Lord as salvation...
There is something different coming for the beloved, the "new heavens and a new earth" where there is no "ungodly," only "righteousness dwells" there. So live in light of that hope "without spot or blemish."1 Then one can have inner peace, knowing he or she is at peace with God (not being one of the ungodly facing judgment, but one of the beloved looking forward in hope to "salvation"). This is because if one gets caught up in "the error of lawless people," then one will "lose your own stability" (v.17), and not have inner peace (even if one is truly one of the beloved).
Not Necessarily Peace with Others
Peace with others believers may (and should) come by living a godly life, but as revealed by Paul's writing to Timothy in 2 Tim 3:122—
Indeed, all who desire to live a godly life in Christ Jesus will be persecuted
So the exact pursuit Peter is arguing for in 2 Peter, to live a holy and godly life, is the same pursuit that will certainly bring a lack of peace with other people who do not desire the same.
Holy and godly living coupled with expectation and desire for the judgment day of the Lord are grounds for having inner peace that one is at peace with God. One cannot have true inner peace without first knowing there is reason to believe one is at peace with God.
1 The only way to be "without spot and blemish" is through the knowledge of God (2 Pet 1:3), by whose power one escapes corruption of the world (v.4) and can build upon faith (v.5-7), and be fruitful for God (v.8), remembering that Christ has cleansed sin (v.9), and that in such building on faith, one will "never fall" (v.10), and find "entrance into the eternal kingdom of our Lord and Savior Jesus Christ" (v.11).
2 Peter was familiar with some of Paul's writings at least (2 Peter 3:15), but even if that had not been noted, if one holds a unity to Scripture (as I do), then pulling in Paul's reference as it relates to the question here with Peter regarding the type of peace being referred to is still valid.