AFDC (don't know if that one exists any more) or other state aid. If she files for aid in other states, they immediately step in and try to recoup any expenditures from the non custodial parent. This can cause headaches unbelievable.
If the mother of the child sitll lives in your state, then she is committing fraud by filing in other states. If she doesn't live in your state, then perhaps (putting the kindest take on this) she simply does not understand that the original court retains jurisdiction unless both parents ask the court to withdraw in favor of another state.
My aadvice, if the mother still lives in the same state and has not moved from the state at any time, is to contact your state or district attorney and file a complaint that she has committed fraud.
In the meantime, regarding the child support problem, I suggest you get a copy of the court order regarding child support and get a print out from the child support office of all payments collected and distributed and send these with a letter of explanation to the other states.
You should also contact the court with jurisdiction asking it to intervene. They may be able to help you.
Having gone through tons of garbage with the mothers of my husband's two children through age 18, I can tell you mix ups will happen with the child support systems we have in place. I have learned NEVER to rely solely on the lawyer. Your son needs to keep really good records and a dated journal of everything that happens. Do the research yourself. Document EVERYTHING. Make friends with the people who collect the child support payments. They will go to bat for you when there is a question about whether or not you made a payment. Always consult with your lawyer before taking any action.
If your son is able to, and feels that his child is not in the best place, then get all of your ducks in a row, and make a good strong case before petitioning for custody. The custodial parent will ususally retain custody unless there are compelling reasons to change it. Does your son have regular visitation? If not, file for that first...
If your son establishes a record of responsibility and integrity with the court, it will give him an edge in every action regarding this case in the future.
Keep up posted on what happens.
On edit: finished a sentence I left dangling...
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