drmac - I have been in this situation and still am. I didn't leave my husband.
We are 3 years down the line now and our marriage is strong again.
Quick description - husband had a short affair and the OW got pregnant. We had no contact with OW or the child for the first 18 months of her life. OW didn't want us to and I didn't want to be dealing with the OW and child while trying to get over this affair (not to mention I was also pregnant myself, this had happened before OW notified H he could be the father of her child) That might make me an evil person but it was the best thing for us at the time. The child was still a baby and knew no different.
We had 18 months of repairing our marriage, welcoming our child into our family, me trying to recover from everything until we decided that we would approach the OW for contact with the child. But we had our terms as well.
My H would never be alone with the OW during contact. We asked for a third party to be present at first while the child was getting to know my H, it turned out to be OW's Mum. I would be included from very soon on in the contact because the child had been born into our family (which OW helped make the situation like this herself, by getting pregnant with a man she knew already had a wife and children) ... my family were not going to be slowly integrated into the child's relationship with her Dad. It was best for the child to be introduced to the "norm" from the start, so on the second contact visit I met the child with husband at a local park and within a few weeks she was coming home with us to share a couple of hours with our children in our home.
All contact with OW went through email which I had access to and OW has my mobile number for emergencies or queries which need answering quicker than an email.
This all helped our relationship and had no effect on the child at all. Pretty much tough on the OW and how she felt about it. She didn't factor in the decisions and my H made it very clear to her that although she may have only been thinking in the child's best interests, he has his family to consider too so their priorities are different some what.
We have managed to repair our relationship because my H took responsibility for what he did. He went to individual counselling. Never tried to blame anyone else, not even the OW, which in the very early stages used to annoy me because like you, my anger for her was more intense than that for my husband (and having spoken to many couples in this horrible situation, that is entirely normal. Perhaps not rational, but normal). H has been completely open and honest with me regarding everything to do with the OW since then. If he hadn't then I wouldn't still be here.
Anyway, 3 yrs down the line, we have regular contact with my step-daughter. She missed out on 18 months with her Dad but she knows no different at the moment. It hasn't affected her in anyway we can see yet. She has a close bond with her Dad, me and her half siblings. She is part of the family. Things would be soooo much easier if the OW disappeared off the face of the planet but that's not likely so I just use my friends to rant to about the OW and try not to spend too much time discussing it with my H as it just causes friction in our relationship. Basically we just get on with it and try to pretend it's a normal "step family" set up.
To add I am always civil to the OW in person. We chat. We wave hello if we pass each other in the street. I will always hold my head up high knowing I have done nothing wrong and I hope the children will grow up knowing that.
Wow, that was really long sorry.
If I were in your shoes, I would not do anything about pushing for contact with the child until your baby is here and settled and the child is older and not so reliant on Mum for contact sessions any more. If my H had had contact with his daughter while she was still a baby, it would have been inevitable it would have taken place with OW present. I wouldn't have been OK with that, nor would he because he didn't want to hurt me any more than he already had.
People are always going to condemn for him not having a relationship with his child if that's what he chooses. This is a horrible situation though and in some respects, would it be better for a child to grow up with their Mum and a possible new partner ... than be bought up in the middle of a hostile situation, where Mum and Dad are at each others throats, knowing that they are a product of an affair, knowing their presence causes hurt ... that's not nice for a child and unfortunately, not all adults can be mature enough and sensible enough to be civil for the children's sake. If your H decides he doesn't want contact, that is up to him. Your decision then about whether to stand by him. But it doesn't have to be decided right now. The child is still young. Maybe with time he'll be open to contact. But having contact opens up a whole new can of worms and it will depend on how the OW will react.
Sorry this is so long. Any questions, just ask. I really feel for you. It is one of the most horrible situations to be in. No matter what you do, someone will be hurt. x
Also you are only a year in. In terms of affairs, that is not a long recovery time. It can take much longer.