Hi Limoncello! Please remember that while your husband cannot oppose you moving closer to your family while you are pregnant (since the shared child doesn't exist yet in the eyes of the court), if you wait to move until after you deliver, he can (and seems WILL) file in court to stop the baby from moving. I would hope your attorney has been clear with you about this? It's quite important that you move SOON, get a doctor in your new city/state, establish yourself in that state, and settle there BEFORE the child is born. If he then chooses to follow you to have more custody time, that is his choice, and that's great. He'll then have a long distance custody plan with the OW's child if he chooses to be involved. If he stays where he is now, he'll have a long distance custody plan with your child and can have more day-to-day involvement with his other child. That's his choice.
I see HUGE red flags about seeing his child "everyday." In even the most peaceful and warm co-parenting relationships, it is not common to see one's child every day if you are not the primary parent (and even if you are). Sadly, divorce means sharing the child, while also remembering that a child is not a possession, and that the custody agreement benefits the child, not just the parents. I can promise you, if you choose to divorce him, you will not want him in your home every day when you are post-partum, healing from child birth and potentially working on breast feeding (if you choose). If you breastfeed, you'll legitimately have your breasts hanging out much of the time those first few weeks as you and baby both figure things out-- nothing is more intimate than this post-partum time, and you won't want someone you do not trust around except on his scheduled visitation time (for newborns, this might look like 2 hours a day/3-4 days a week).
Please remember that a custody order protects both of you AND YOUR CHILD. The more specific a parenting plan, the less chance there is for conflict between the parents. The less conflict between parents, the happier and more secure the child. You and STBX can deviate from the parenting plan occasionally as it works for you both, but you always have it to fall back in during times of strife. Also, each state has standards for parenting plans, depending on the age of the child. You need to know from an attorney in the area where you plan to move, what a judge is likely to order/approve for a newborn, and then go from there in your offerings to your STBX. It will be in your new area that you'll be filing for custody and child support.
Also, in many states you cannot legally divorce while pregnant, but I'm assuming you're not in one of those states? I cannot imagine the benefit of waiting until the baby is born to divorce, because if you divorce now you'll have spousal support figured out and the divorce finalized, and then just have to worry about parenting plan and child support. Being newly postpartum and figuring out divorce, spousal support, custody, AND child support is a lot. As many of us can tell you, postpartum hormones are no joke and they stick around for up to a year. Having things sorted now, when you're clear headed (well, as much as someone whose gone through this trauma can be) and able to focus on what's best for you and the baby would be ideal. Your STBX may not be worried about the baby being born "out of wedlock" (unless he's truly deeply religious, but that doesn't jive with an affair so...), but rather trying to stall in hopes you'll change your mind.
Lastly, your STBX may be a good person, but he's a deeply broken person based on his decisions. He didn't make mistakes, he made conscious decision after conscious decision to betray you and ruin his family's life. Until he understands his "why" of having an affair, until he's done that deep introspective work needed, he'll never be a safe partner. Maybe he'll come to you in 6 or 9 months or 1.5 years from now with that "why" information, and then great, you can consider reconciling at that time. But right now, heck no. Affairs don't "just happen" or "just continue." He better dig into his why before he attempts any further relationships.
I know that was a lot of info. I've been following along and cheering for you but not commenting, but I wanted to be sure you were clear about moving BEFORE the baby is born and the rest just came out. :)
Best wishes and take good care.