I wouldn't expect that you would have gotten anything from the IRS. Filing an injured spouse claim is what you do when you file jointly and don't want your own refund to get sucked away with his. Under federal law, the IRS is required to take all of a tax refund if there are child support arrearages.
BUT there is something completely different that may help your family. Is the back support owed directly to the mother or is it owed to the state because she was on public assistance? Child support is a debt just like any other. If the money is owed to the mother, she can forgive all or part of a debt or she can ask the state to stop enforcement action on her behalf (of course if she's angry or a jerk, it won't help). If the money is owed to the state, most states have debt forgiveness programs. That he now has another child to support may be a basis to re-calculate (and thus reduce) some of the back support. I don't know what that program may be called in WY, but ask at the local district office.
One last thing: have you had the child support modified to take into account the new child he has to support? That may be a bargaining chip with the mom of the other children, reduce the back support or we'll ask the court for a reduction based on having another child. Although, before you make that threat, talk to a local family law attorney to verify how likely it is his support would go down significantly.