Wow...
I really feel for those kids. I would sincerely suggest getting an order of protection of some type against their Father (at least for the boys). You may need to sit down with the boys and explain to them that if they will go in and tell a judge what their father did to them, they will be safe and he won't be able to hurt them because of it. Maybe if they know he can't hurt them, they'll be more inclined to tell a judge the truth.
Also, I'm glad you're seeing a new attorney. It sounds like the person you were seeing is incompetent. Explain the situation to the new attorney, see what he says (and please post back here so everyone who is concerned for you & these kids will know what's going on).
One more thing...you said that he has state insurance for the kids, right? by state insurance, do you mean medicaid? If that's what he has, he's full of it, cause Medicaid pays for anything and everything medically necessary. The copays average out to be roughly $5 per doctor visit with a prescription. That's here in Colorado tho. Not sure about where you are, but since medicaid is pretty much universal, I wouldn't think there would be much of a difference. In the order that requires him to pay for part of the insurance does it state that he is to provide you with copies of the medical cards? If so, talk to your CSE caseworker(if you're involved with Child support enforcement) or take him to court for contempt based solely on that. Then you'll have the medical cards, and you'll be able to contact the insurance to find out what exactly they cover. Just something to try.
I wish you and your wife and kids the best of luck. It sounds like this guy needs a swift kick in the pants.