I don't see this relationship lasting. If he has an 18 year old my assumption is the LW is likely at least in their 30s if not 40s (and the boyfriend in his mid-40s). Celebrating a 1 year dating anniversary on the actual day is not a "need", not realizing that by 30 is a serious issue. He can spend time with his daughter and take LW out to celebrate on one of what sounds are the many days when he doesn't get to spend time with his children. 

That the LW thinks the issue is somehow tied to the ex-wife only furthers my opinion that she's immature. Too immature to be in a serious, long-term relationship. He does not seem to be someone controlled or manipulated easily, good for him.