Hugs to you. I know a little how you feel, except I am too old to have more children and FWH and OW and WH refuse to have a DNA test. I too married last year to my partner of 8 years, knowing that he had conceived a son on an ONS 2 years into our relationship ( although it took him 3 years to tell me).When I married him, i thought it was all over and he didn't see OW and OC except for work. A month after our wedding, I discover they still go out on work night drink sessions and he has been seeing the OC. I can relate.
It is absolutely devastating. I have insisted on NC with OW and contact with OC to be arranged through OWH ( who knew all along and doesn't seem to care that he is raising my Hs child as his own). I think you could insist on NC with OW and with OC. Is she married? Does her H know? Does she want financial support? I would say no finance without DNA test. I believe it is advisable for you to get your claim in first to protect your C. Have a look on the OC thread in the I can relate forum. There is a lot to read there, some helpful.
I don't understand how you have ONS with someone when you love someone else, but this site tells you we are not alone. That is the hardest part, as I (and you) thought everything was wonderful. Why do they do it? I am learning (see Healing Library) that it is very rarely to do with the BS or the relationship. It is something in them. In my case alcohol was also involved and I too think he can't have been that drunk as he wouldn't have maintained an erection. Your WH needs to focus on making you feel safe and secure and loved. He needs to work on why he did it and what boundaries he will set up with women in general, so that he never does it again. If he does worry on this for you and you C, then R might be possible, but he has got to work at it.
This is awful for you. I love my husband and apart from 10 stupid minutes everything is great. I am trying to get to the stage that I don't want those 10 minutes to ruin everything else we have. Too right, he (my H and your WH) was wrong to have the ONS, but OW has compounded the situation. She could have taken precautions in the first place, she could have taken the morning after pill, she could have had an abortion. Continuing with the pregnancy has compounded one stupid error. She chose to continue the pregnancy without reference to your WH. He has had no decision in anything that happened after the ONS. You can castigate him for the ONS, but she has continued the situation. She should not have continued with the pregnancy, if she can not afford to raise the child herself. She should not have had sex without taking precautions unless she was aiming to pregnant.
Try to separate out what has upset you about your WHs actions from the OC situation (very difficult). You have a plus in that he doesn't want to maintain contact with OC - my FWH is still working on that one, which upsets me.
If he definitely is the father, then he probably does have to support financially which is really tough. You need to ask him what he is going to do about that. No way should any of your personal money fund the OC. Will he take a second job? He can provide financially without having any physical contact. He needs to step up and show you that you are the most important woman in his life (and your child) and he is going to keep you safe.
Good luck, do wha they all say on here, take care of yourself, drink plenty of water, get our sleep (as much as you can with a newborn).