I am so sorry you find yourself in this situaiton. I strongly encourage you to go to counseling on your own. I am not in the exact situation - I sought therapy because I wanted to deal with my own history. But my history affects my relationship with my husband, and frequently my therapist and I work on how I view him, how he pisses me off, and how I communicate to him in good and bad ways.
The reason for you to go is threefold. First, you can learn ways for you to communicate with your husband better. That doesn't mean he will be receptive, but it may help. He has issues and you need strategies to get through to him. It also lets you look objectively at yourself - do you understand your husband's persepective? Do you do things to make the situaiton worse? Do you increase the distance between you? Regardless if he is now acting like a jerk, it doesn't make it okay to shut down and fixate on blaming him. For instance, you say you didn't mind when he left your bedroom at first. When and how did you invite him back? Clearly I don't know you, but I know that therapy shows you things about yourself you can't alsways see on your own.
Second, if you go and make an effort, you might be surprised that he is more willing. If there is actually an appointment on the calendar, and you ask him to go with you to "Your appointment" - that's very different then saying he needs marriage counseling. Sometimes the delivery or wording of the invitation matters.
Third, if the marriage ends, I believe it is good to document your husband's behavior and it's impact on you. It could probably be argued tha the has caused and estrangement (moving out of the bedroom) and this has had a profound impact on you and your marital relationship. It is also good to show that he was unwilling to work on the marriage, whereas you went to counceling and were working on the marriage.
Hearing your side, your husband is acting self-absorbed to say the least. He also sounds a little depressed. I think a lot of marriage problems are due to unmet expectations. I wonder if you and he had radically different expectations of parenthood (actually having the child) and of what your roles would be (like who would be promary caregiver). My guess is you both did not understand each other's expectations prior to having a child or one of you has changed and broke promises.
Either way you need to set some clear expectations and rules about how to parent, and a therapist can help you sort out the differences of opionion. Therapy is really setting strategies for success. This can be true for your marriage, but also to parent (and may still be needed if you seperate - it won't get any easier to parent if you divorce).
Having a child can cause more stress on a marriage than anyone can envision. And if there are pre-existing issues a child can make those worse. I will say, I think everything gets easier after the first three years, but that was jus tmy experience. Hopefullly you can work this out, but even if you can't, your husband needs to engage with his daughter more. He is missing out and so is she.