It sounds like perhaps the D might be claiming that OP’s house is her primary residence and using mom’s lower income to file for FAFSA. We don’t know, however, whether the D has ever received any FA as a result of filing. I file every year and only once received $500 because I had two kids in college. If I was the OP, I would try to get a copy of the FAFSA form that was filed.
Another thing to look at is the divorce decree. In my state, if one or both parents have college or professional degrees child support and/or payment of college tuition is often ordered. The theory is that kids of divorced parents have enough bad stuff going on that they should at least be able to achieve the same level of education as their least educated parent. Thus, in many cases, parents are responsible for children past HS graduation age, but only if in the decree.
The credit check is a good idea in general but I don’t think it would show the FAFSA use.