She sounds like a person who doesn't deserve being fought for. What kind of a woman decides to leave her child because of some misunderstanding in a relationship? And even if she does, that's not how people deal with problems, running away is never a solution. If she's this kind of person even if you don't split up now there might be a time when you eventually do because she wouldn't want to fix the issues and she will run away. And with a kid being raised up it will be harder for both of you to go your separate ways and it will be a bigger tragedy for the kid. In your situation at least you wouldn't have to fight for your child and when she suddenly decides that she wants to raise it you will be in a privileged position as it's her that abandoned the family.