Are there any mods (or some other method) that would allow us to give gear of any sort to children? If I was raising children in the hostile environment of Fallout 4, I would have them in armor before they could walk and they'd be training with and carrying firearms from the age of three.

Odds are they don't have skins for most of the clothes and armour ingame. ChildRace is separate from HumanRace.

Maybe when the GECK comes out... There are clearly several clothing options for kids which we might be able to add ballistic weave to at the least. Someone surely will add the Red Rider BB gun to the game, which 'clearly' should be carryable by kids (and I hope to be able to mod the crap out of them so they can actually be slightly useful for kids defending themselves from the dangers of the wasteland).

What about giving them a Laser Gatling Gun?