I agree with what others have said. You know that 'he's just not that into you' book? It looks like he's just not that into you, or more importantly, not into his daughter either, which is a tragedy.
It's not about him dating other women, it's about providing you with partnership, love and support. That soon after the birth of a child, a good man assists the mother of his baby as fully as he can, and does everything he can for his child. Being a father may not be what he wanted, but you didn't plan it iether and you're meeting your commitment to her. Fatherhood is independent of who you're sleeping with. It's a commitment he can't and shouldn't get out of. If he won't pay with time and attention, he can at least pay child support. I know you don't want to fight with him when you're still hoping he'll come around, but I think you need to do it for your and your daughter's long term welfare. And your ex husband too. Perhaps your parents will help you pay for a lawyer to settle up with both your men.
I know it's hard, especially when you want him to love your daughter (and you) but it looks like it's not in him. He may just be that selfish, in which case you're well shot of him. I suspect once you've had some time on your own, you'll get in touch with your own anger about all this and find an easier time fighting for what you need and what is fair. He's not the only guy in the world.