The QEE is ‘paid’ by the student (student’s responsibility). Since the student is a dependent, the parent gets the credit.
If the father takes the AOTC and gives it to the student, he’s really reimbursing the son. It’s the IRS that makes the rules that say the AOTC credit goes to the parent and the school that says the student is responsible for the payment of tuition, etc. Just try getting to see the bill if your student doesn’t allow it. It’s not your bill.
Your ex would have to know all the billing and taxes of your son to do it. It is kind of circular and I found I had to do my taxes with my kids’ because of credits and taxes owed on scholarships. There was stuff from my taxes (tax rate) I had to fill in on my kid’s taxes, and stuff from hers needed for mine for the AOTC. It is different now because the taxable scholarships is not based on the parent’s tax rate but on the estate tax tables. I’m done with that so don’t know if each return can be prepared independent of the other.