Another thing I wonder is if maybe this level of thieving is actually a relatively new occurence among the children. They've been on the road a lot, not had much opportunity to interact with strangers, so not much opportunity for theft. They probably snatched some stuff from the adults, but in the cave they didn't exactly have a great hoard of personal objects if I recall correctly. And they probably only stole small things anyway, since they wouldn't have much chance to keep anything on the road. So up to now any theiving has probably just been brushed off as a minor nuisance at worst, if it was noticed at all. It's only now that they have other potential marks to steal from, and that it's becoming at all apparent how far they're willing to push their luck.
Also, I always find it weird how impassioned people can get over not being able to kill kids in video games. I get the principle behind it and for that reason I support it if I'm asked, but it never stops feeling like a strange place to so firmly plant one's flag and have strong feelings about.