If your son lives with you for more of the year (more overnights) than with his father, your info is used for FAFSA. It doesn’t matter who takes the tax deduction.
Under the new tax law, it really isn’t that advantageous to take the tax dependent, usually just one $500 credit. If the father really makes $180k, probably won’t qualify for the AOTC anyway (the student must be a dependent to get that benefit).
If he can get a tuition benefit at a Jesuit school, go for it.