That said, I think that you are definitely not overreacting, but you [i]are
The reality is that your boyfriend has a lifetime commitment to a daughter with a chronic illness. He is going to be connected to his ex, who is his daughter’s mother — for life. And while you think he’s contacting and engaging too much with his daughter’s mother, the reality is that this is what works for the three of them. And the reason I know it works for them is because they continue their dynamic, and while your boyfriend makes time for you, he puts his daughter first, and sometimes, he puts his daughter’s mother ahead of you, too.
When he defends himself to you and says he’s getting together with his daughter and her mother for the daughter’s sake, I believe him. Divorce or parents being separated is not what harms children — parental conflict harms children. If these two parents can make things work for their daughter, for her sake, then they’re doing the right thing. When you date a single parent, you’re never going to be number one all of the time — and when the child has special needs or a chronic illness, you’re going to be number one even less of the time.
It’s really great that you found all this out so early in the relationship because clearly, this dynamic is not going to work for you, and clearly, he’s not going to change things. If you continue to try to change him or get him to change, or tell him how he should be doing things and that he’s doing things wrong, he’s going to get angrier and angrier, and so are you.
The fact that he lives 3000 miles away from you is a problem, and the fact that you’re 32 means that you probably are looking for a serious relationship that will lead to marriage and children of your own. By getting further involved with this guy, you’re setting yourself up for a relationship that is not destined for success. My advice is to move on and find someone who is more compatible with you in more ways.