I haven't read all of the second post. You do need to talk with a lawyer. It is best to have custody papers giving you full custody before any visits occurr. Because your ex has equal rights to the baby with you. Actually he has legal rights to both children.
If you do not have custody papers filed with the court and wish not to do that then take some precautions for the visit. First it is reasonable for you to set a date several weeks after delivery. Then at the time of the visit have a friend or two present in the house. They don't have to be visible. They're there to help you if you need them.
If you have an amicable relationship then filing custody papers is still needed for all of your sakes. Filing doesn't need to ruin the relationship. There is a lawyers office on Glisan close to the 60th st exit from I-84 that has a sign saying that they provide mediation and friendly divorces. You might check with them. If you can't afford an attorney check with Legal Aid. I know that there is usually a waiting list but perhaps you can get advice to get you started.
If you and your ex are able to talk without arguing how about telling him of your concerns? sometimes that relieves some of the tension.
I had a foster child who was ordered by the court to visit an aunt and uncle in their home. They had custody of her brother and were open about stating they wanted custody of her. We had visits but I was always present in the same room not only because they might keep her but also because I was concerned about what they would tell her. I'd already had experience with her mother telling her lies. I eventually adopted this child. Once I had legal custody of her I wasn't as concerned because the court would arrange for her return.
Agreements did to be writtin down and filed with the court. If you have a court order giving you full custody the father will have comitted the crime of kidnap if he were to take his own child.
The only way that you can know if any of the legal advice you get here is accurate is thru talking with an attorney. Perhaps you're just wanting logistical advice because you already have a custody agreement filed with the court. I hope that is the case.
If there isn't parenting time in the agreement you don't have to let your visit at all. I do think in most circumstances it's better for the child if you do. The advantage you have in this case is you can name the date, time, location. Do that when it's most convenient for you, considering your health issues. You can even require that he visit with his older child before he can visit with the baby. I think this is important to do because the older child will feel left out at the visit including the baby. Babies always get the most attention.
You can arrange the visit with the older child to be done at another relative's or friend's house. You can even ask that it be supervised by a professional person. Long ago Waverly Children's home provided space and a supervisor for such visits. There are also private people who will do this.
I hope that you can get this worked out so that you have as little stress as possible. Giving birth and then finding a workable routine with a newborn is as much stress as you should have. Perhaps it could help for your doctor to prescibe a period of time during which it's best for him not to visit? I don't know if that would help. Again, the advice of an attorney would be helpful