OP, please, please, please look into the resources I have provided (ARC and Shirley Glass). I am thrilled for you that you have met with your priest. Priests are wonderful resources, but few are experts on affair recovery. The fact that in your first meeting things turned into “what is wrong” with you, is a good indication that your priest doesn’t understand this dynamic. (During recovery, yes you will need to address deficiencies in the marriage, but that is not the first priority.)
Your husband’s first task is to do whatever you need to begin to feel safe.
How long ago did he tell you about this? How long has he known about the child? And does you believe that he wants to keep your marriage? I am stunned that he thinks he can tell you a month before the child is due and then expect to be a normal dad to this child.
These are very important questions for you and can help you know how to proceed.
In regards to the baby, again please read the Glass book. I know that she discusses how to work through this. I believe that I am passing on her advice, which is why I would want you to verify. Until it is proven that your husband is the father, he should have NOTHING to do with him or the mother. He shouldn’t talk to her or about her to anyone but you (and counselors/priests). He should block her from contacting him. (Normal recovery periods include a time period where the injured spouse has full access to all of the involved spouse’s accounts.) Until proven otherwise, this is not his child. Together the two of you can figure out who will contact YOU about the delivery so that you can proceed with testing. (Personally, I wouldn’t spend extra money for a pre-birth test. First of all, your husband is going to spend a lot of money on this child if it is his, and second, it sets some precedent that he isn’t her go-to person.)
If the two of you agree that he can be a part of this child’s life, then (I believe) Glass recommends that all communication about the child goes through you or someone you trust. Your husband and the mother should not have any contact. Since she doesn’t seem willing to place the child in a two parent home, then if she wants your husband’s involvement, it includes you. Start talking to him and your priest about Baptism. (My opinion here) I think that given the scandal and your children, it should be a private and quiet ceremony.
I continue to pray for you…