There seems to be several problems here, not just one.

1. It sounds like he has trust issues
2. He confuses the relationship with the mother and the relationship with the child

I would certainly suggest individual and couples counseling.

In answer to your questions, no, you are not cold for being angry at him. There are plenty of men that will step up as step parents without a single thought. He should be happy to have a daughter and not concern himself with the who or what. Right now, I would say that filing for sole custody would probably not be that great. At least make it his decision to be involved. If he's a deadbeat, then you've done what you can, but she'll always want to be involved with her "real" dad even if you get married later.