Since your name is law questions I will answer that first. I think Child Support should stop as soon as the child isn’t primarily living with you. I swear I saw it in NC GS 13.4 sometime.
I believe the IRS is of the following opinion:
You can claim your child if
- you (and your ex-spouse’s child support counts for you) paid more than 50% of her expenses that year
- she spent more than 50% of the nights with you.
(I simplify somewhat, but you get the idea I hope.)
If she moved out today and moves back in around October then you are good. If they break up at Christmastime then I suspect you can’t legally claim the dependent.
I don’t think the boyfriend’s parents can claim her unless they adopt her.
Clearly it is immoral for you to collect Child Support payments when you aren’t using the money for the child. However, men are used to that and expect it.
There is also the ethical question of not informing her father about important events in her life. I’m sure I could go either way on that question. No one said being a parent was easy.