Thanks for the advice everyone!
I managed to talk to my accountant today and she says if my monthly fee for the kids is say, $1000, than I would issue the full monthly amounts on one receipt regardless who pays. I am obligated to provide both parents with a receipt if they request it but it is the exact same receipt, no modifications what so ever. It is up to them to figure out how they will claim the kids and it leaves me out of it.
I think this is what I'll do since payment for the first couple months came from mom but dad says he paid her and mom says no he didn't so this way will at least keep me out of that he said/she said as well.