I have friends in a very committed relationship who never plan to get married. My husband and I almost didn't get married, simply because it felt unnecessary. We decided the legal benefits were good enough, so ended up getting legally married, but it didn't change our commitment level. Marriage has its benefits, but it isn't the only thing that signifies commitment. I agree with Nichelle, it sounds like it's time to have a heart-to-heart with your boyfriend. Think about WHY you want to get married, what marriage means to you, and consider what a committed relationship, including co-parenting, might look like for you outside of the institution of marriage. Ask him about his commitment, what marriage means to him, and what a committed relationship including co-parenting means to him.
It's okay to step away and come back to convo if either of you start having difficult emotional reactions or feel the need to get defensive. It could be a good opportunity to try couple therapy, just have someone who can mediate the conversation and who will be able to ask the right questions. Remember that the goal either way is not to convince him to want to marry or to convince you to not want to marry. The goal is to come to an understanding, for both of you, and to, hopefully, create and continue a healthy relationship
4yr is a long time , .. maybe you know he doesn't want kds or marriage? Ask him. How old are you though? Marriage matters, because most ppl that enter a marriage, want to because of commitment etc but if he doesn't want to be a dad and isn't a dad and want to be called Bob etc by his name then.. he's not there or going to get there if he's playing uncle or friend to your daughter. Tough one. It's not too late if you can afford being alone and finding someone else. Don't worry about the 2 dads.. just don't keep doing the move in together and live together. It will break her spirits. But also we don't know how breaking up with him will change you as a mum to her, you may get more irritable, annoyed, depressed and stiff... lot to think about
If she sees him as her father then what would change with you marrying or not marrying him? Sounds like you should sit down with him and have a conversation about how your feeling and to get some clarification