While τεκνία has the sense of "kids"...:
τεκνίον, ου, τό (Epict. 3, 22, 78; Anth. Pal.; PFlor 365, 15 [III
A.D.]; POxy 1766, 14; TestJob, ApcMos) dim. of τέκνον; (little) child
voc. pl. τεκνία; in our lit. only in the voc. pl., used by Jesus in
familiar, loving address to his disciples, or by a Christian apostle
or teacher to his spiritual children τεκνία J 13:33; 1J 2:12, 28; 3:7,
18; 4:4; 5:21. τεκνία μου (TestReub 1:3; TestJob 5:1 al.; ApcMos 5:30)
Gal 4:19 v.l.; 1J 2:1.—DELG s.v. τίκτω C. Frisk s.v. τέκνον. M-M. TW.
Arndt, W., Danker, F. W., & Bauer, W. (2000). A Greek-English lexicon
of the New Testament and other early Christian literature (3rd ed., p.
994). Chicago: University of Chicago Press.
παιδία (actually, παιδίον) refers to a very young child, up to 7 years:
παιδίον, ου, τό (Hdt., Aristoph.+) dim. of παῖς (Reader, Polemo 274,
w. ref. to Hippocr., Sept. 5 and Philo, Op. 105: a very young child
‘up to seven years’; B-D-F §111, 3; Mlt.-H. 345). ① a child,
normally below the age of puberty, child ⓐ very young child, infant,
used of boys and girls. Of a newborn child (Diod S 4, 20, 3; Just., D.
34, 2 al. [after Mt 2:8f]; Tat. 33, 3) Lk 2:21 v.l. (eight days old,
as Gen 17:12); J 16:21. Infants are fed honey, then milk B 6:17 (cp.
Diod S 5, 70, 3 αὗται [αἱ Νύμφαι] δὲ μέλι καὶ γάλα μίσγουσαι τὸ
παιδίον [τὸν Δία] ἔθρεψαν.—HUsener [at γάλα b]). Those who are born
again have ὡς παιδίων τὴν ψυχήν a soul like that of newborn children B
6:11.—Mt 2:8, 9, 11, 13f, 20f; Lk 1:59, 66, 76, 80; 2:17, 27, 40; Hb
11:23 (cp. Ex 2:2f). GJs 20:3f; 21:3; 22:1 v.l. (for βρέφος); 22:2
v.l. (for παῖς). ⓑ w. ref. to age (ApcEsdr 4:33, 35 p. 29, 9 and 12
Tdf. παιδίον … γέρων): Mt 18:2, 4f; Mk 9:36f; 10:15; Lk 9:47f; 18:17;
1 Cl 16:3 (Is 53:2). Pl. Mt 11:16; 19:13f; Mk 7:28; 10:13f; Lk 7:32;
18:16 (on Mk 10:14, 15 and parallels s. JBlinzler, Klerusblatt ’44,
90–96). γυναῖκες καὶ παιδία (Num 14:3; Jdth 7:23; 4 Macc 4:9; cp.
Jos., Bell. 4, 115) Mt 14:21; 15:38. παιδία … πατέρες … νεανίσκοι 1J
2:14.—B 8:1ab. Of girls Mk 5:39–41; 7:30. ⓒ w. ref. to relationship;
the father is indicated by a gen. (μου as TestJob 39:12; cp. Epict. 4,
1, 141 σου; TestJob 4:5) J 4:49. Pl. Lk 11:7. The child indicated by a
gen., w. the father ὁ πατὴρ τοῦ παιδίου Mk 9:24. ② one who is open to
instruction, child, fig. ext. of 1 παιδία ταῖς φρεσίν children as far
as the mind is concerned 1 Cor 14:20.—W. ref. to their attitude toward
the truth (Artem. 2, 69 p. 162, 7: τὰ παιδία ἀληθῆ λέγει· οὐδέπω γὰρ
οἶδε ψεύδεσθαι καὶ ἐξαπατᾶν) Mt 18:3. ③ one who is treasured in the
way a parent treasures a child, child, fig. ext. of 1 ⓐ of the
children of God Hb 2:13f (vs. 13 after Is 8:18, but understood in a NT
sense). ⓑ as a form of familiar address on the part of a respected
pers., who feels himself on terms of fatherly intimacy w. those whom
he addresses (Cornutus 1 p. 1, 1 ὦ π.; Athen. 13, 47, 584c) 1J 2:18;
3:7 v.l. Used by the risen Christ in addressing his disciples J
21:5.—B. 92. M-M. TW.
Arndt, W., Danker, F. W., & Bauer, W. (2000). A Greek-English lexicon
of the New Testament and other early Christian literature (3rd ed., p.
749). Chicago: University of Chicago Press.
The distinction between the two may suggest affection.
As to "idols" I suggest that what he has in mind are not stone figures and such but rather mental constructs. That is, his concern in writing the letter is with those who construe Jesus as being almighty God. We see him damning those who deny Jesus' humanity:
ISV 1Jn 4:2 This is how you can recognize God's Spirit: Every
spirit who acknowledges that Jesus the Messiah has become human—and
remains so—is from God. 1Jn 4:3 But every spirit who does not
acknowledge Jesus is not from God. This is the spirit of the
antichrist. You have heard that he is coming, and now he is already in
the world.
This "God-Man" was also the idol that Paul predicted and decried here:
2Th 2:3 Do not let anyone deceive you in any way, for it will not
come unless the rebellion takes place first and the man of sin, who is
destined for destruction, is revealed. 2Th 2:4 He opposes and exalts
himself above every so-called god and object of worship. As a result,
he seats himself in the sanctuary of God and himself declares that he
is God.
So to "abstain from idols" one must concur with "John" that Jesus arose from humanity and is not himself God and concur with Paul and not embrace the God-Man (who is a mental construct, not a real being).