I will make a few suggestions with two central facts in mind. First, odds are VERY good that your kids will lose or break these knives in time. That's ok. How many of US still have our first knives? With this in mind, I'd stay under $40 max and that's easy to do - there are a lot of great affordable knives out there.
Second, your boys WILL cut themselves. Buy some Band Aids. Again, I think that's ok ..... a nip now will help them learn respect for the tools and learn how to handle them with skill and care. And again, how many of US have been cut?
Now, for my suggestions ... if your kids would prefer something more modern and "gadgety," get them a Victorinox Swiss Army Knife. Specifcally, I'd opt for the
84mm version of the
Tinker. I don't like the "my first SAK" or the kids Opinel because I consider them marketing gimmicks designed to make a buck off nervous-nelly moms. And how long till your guys are embarrassed to be carrying a "baby knife?"
If your kids would be more into a traditional slipjoint, some good affordable options are the
American-made Buck 303 stockman, and just about ANY knife from
Case. I think the Peanut, the small Texas Jack, or the medium stockman would be good choices for small hands.
Now, on locks ...... my preference would be a slipjoint, not a locker. This will help your "young men" learn careful, responsible handling of a knife.
On steel ....... there are two trains of thought: These are kids, and kids aren't going to be that responsible, so better to get them easy-to-care-for stainless steel. Or: These are kids and they should learn how to take care of their things, so a good carbon steel ("CV" in Case's case) will help them learn how to do that since they'll have to keep them clean and dry and oiled. When I was a kid I used to LOVE to rub down my carbon steel knives with steel wool and naval jelly and then slosh 3-in-1 oil all over them. Most of my jeans probably had oil stains in the pockets.

Anyway, I don't think there's a "wrong" answer here. If you do decide on carbon, look for a
Case knife with a yellow handle (most, not all, of their yellow-handled knives are CV),
amber bone handle (most, not all, of their amber bone-handled knives are CV), or a
Red (CV) handle. Boker also makes some good carbon slippies these days.
Lastly, please keep us posted on what you choose, how your boys like them, and how their mom deals with it.

My little guy is just 2 now but he shows a LOT of interest in my pocketknives, always wanting to see me cut something. Won't be too long till I'm in your boat.