@cshell2 said that she has too many credits/no tax liability, so she’s not giving up $3000, only $1000 (the refundable part of the AOTC if there is actually $4000 of AOTC QEE).
There are a lot of moving parts in this scenario. Her son might pick a school with full COA or full tuition so there may be no AOTC to claim at all. Ex may also not have any tax liability since he has younger children who he is claiming the full child credit for, etc. etc.
I just threw out the option of having her ex take the son as a dependent and seeing if it worked out better for all of them.