I'm so sorry to hear what you're going through. A very similar thing happened to me about 7 years ago with my then husband. He'd suffered from depression his whole life and he'd been going through a particularly difficult period - changing meds, etc.. - when he suddenly announced he wanted a divorce. I was completely shocked and totally devastated. I couldn't believe after everything we'd been through that he was ending our marriage... I tried literally everything, but it was all in vain.
Many people questioned whether he was having an affair (nothing else made sense), but I refused to admit this was a possibility and he adamantly denied it. Despite everything else and the absolute betrayal and anger I felt, I did believe him on this point alone. I'll spare you the gory details, but I eventually caught him in a lie and found out that he was, in fact, cheating. In our case, he didn't want kids at all and I did, although this was something I was willing to give up for him. The woman he was having an affair with (his now wife.. ugh) didn't want kids either. Perhaps this was part of the allure... who knows. I do know that finding a new relationship, or even having someone else express interest, was exciting for him and reminded him of the passion he felt was missing.
I'm not telling you this because I necessarily think your husband is seeing someone else.. but I do think that it's a possibility. My ex also had ridiculous ideas about what a marriage should be, which I found frustrating and difficult to deal with. Whatever the case, you should do whatever you think is necessary to keep yourself (and your DD) healthy. If he agreed to counseling but isn't fully committed, you'll know during the first session.
Many, many hugs to you, Emily. Reading your post brought back the memory of my experience... it hurt so much there were days I didn't think I'd get through it. But I did, and you will, too. Good luck to you and please keep us posted.