This is reminding me of something I heard about recently... maybe here or maybe another group... let me think... One parent was paying the doctors first and seeking reimbursement for half from the other. The other parent would then pay the doctors and the insurer would reimburse her (because she carried the insurance) for the overpayment. She went to the child support people and showed proof that she had paid so the child support people refused to make her reimburse the father. He ended up paying 100% of the bills and she would pay 50%, get a receipt, then get reimbursed for the overpayment. Yep, this WAS fraud.
It took a really long time for the father to figure out what she'd been doing and I don't remember how it all turned out... but...
I'd be careful about making direct payments of more than half of the unreimbursed expenses... I think KGrow's suggestion of getting information about what insurance covered and proof that she paid and proof that she pursued insurance reimbursement first, it might help...
This type of stuff is such a tangle, unless the medical costs are huge, it might not be worth spending lots of time questioning it. And if the medical costs ARE huge, it would suggest to me tht the kids' medical needs are big enough that the father should be more involved, closely enough that this type of mix-up should not occur quite as easily.