What a dreadful situation to find yourself dragged into, utterly humiliating, even though you have done nothing wrong.
This is going to be such a bomb drop in your children's lives.
I can well imagine, despite loving him, that you are wondering do you really want to be a part of this.
Your husband bringing his child to your home, and YOU having to act as step parent in this situation.
I would not rush into agreeing to ANYTHING.
This is NOT on you to make it work.
I would NOT be agreeing to ANY logistics regarding the child.
Any contact will be away from your home anyway for a long time as the baby will be so small, and will need to be with its mother.
How are you going to feel with him spending time with her?
How are you feeling about having this very angry woman in your life for rest of your marriage? ......well at least for the next 20 years as the child grows.
Indeed, it will NEVER be the child's fault, but that does not make you unreasonable to say you don't want to have the child around you, in your home, reminding you of what your stupid husband did.
You are human and I can understand that this may be how you feel, even though you wish you didn't.
I think you should have very, very low expectations that your marriage will survive this.
You were on a break, but the speed with which he went on the prowl is extremely distasteful, but by gum, he surely is paying for it now.
I feel very sorry for you and I can well imagine that your head feels like your head will explode.
However, ultimately, I think the humiliation and distaste of this situation, will cost him his marriage to you.
I think it most likely that as time goes on the situation will chip away at the love you had for him.
So sorry OP, you sound lovely.