I dunno... Thoughts? Advice?
Man, that's a tough situation

Life would be a lot easier if everyone just acted like adults. I mean, everybody goes through tough times at one point or another and it's nice to be able to both get help and give help, but the rest of the family is definitely using you guys through your MIL.
The nice thing about America is that you only fail if you want to. So even if you cut them off, there's still food stamps, government aid, free cell phones from the state, soup kitchens, etc. Your excuse for cutting them off can simply be that you are in some tough financial times yourself (go buy a new Core i7 gaming system and then it'll be true! haha).
So basically, it sounds like the children are acting irresponsibly and are taking advantage of your MIL. As long as she keeps being a pushover (a harsh word, because she is trying to be a supportive mom to them, but they are clearly using her), they aren't going to learn because the gravy train is going to keep on rolling. In that situation, I would halt all funds going in there. There are other avenues for support if they need it.
The one catch is that your wife feels guilty and continues sending monetary support, which keeps getting passed to the other kids, so the cycle continues. I would have a discussion with her about how you want to help, but you also don't want to encourage freeloading, and that alternative means of support are available to help them grow. You don't want those kids to be dependent all their lives, especially if they are 20+ years old already and still mooching off mom.