Sounds like your husband has turned you against his Mom. How he's experienced her does not necessarily determine how you'll experience her. Sounds like she's made some mistakes, one a serious one, and has moved on with her life. Your husband is still expecting an apology. He needs to let that go. It's not going to happen. I understand wanting an apology. I would hope for one. And her not apologizing does affect him if he lets it. I suggest that he needs to let go of that expectation.
Yes, he also needs to let that experience allow him to make better boundaries with her. We don't forget but we have to forgive if we want to live a full life. Her drama in the past has make life unpleasant for him. However, he has a different relationship with her now or he needs to have a different one now. He's no longer dependent on her. He is an adult with a wife and child. He needs to protect them but he doesn't have to shut her out of his life and yours.
The two of you need to decide how you want to be involved with his mother. You can have a friendly respectful relationship with her without being emotionally close. That is the way we should start with all relationships. Friendly and respectful without having preconceived ideas about who they are and how they'll act. Have boundaries. Expect her to respect them. When she's crossing over, stop her in a kind way.
For example about birth control. There is no need for you or your husband to ever have a conversation about that. If she brings it up just casually say that it's a personal decision that you're not willing to discuss. Repeat it kindly as often as needed. No need to get upset. Know that you have the right to not discuss it.
Have your husband tell her that you're both not able to have all four women at your house for extended visits. When you start to get tired, quietly tell them, you're tired and go to your room to rest. It's even fair, if your husband has discussed this with his mother ahead of time to say it's time for them to go for awhile. Give them a time to come back. Or ask that they not all visit at once. They have a hotel to stay at. They can be tourists. They just have to know ahead of time what you expect from them. No need for drama. Smile and repeat as needed.
Your husband could even say that it would be OK for her to bring one other person but that he doesn't want you to get worn out with company.
You don't even know that they expect to all stay at your house all day. Just talk with your mil ahead of time about how you want to arrange your time with them and the baby and your husband. This is one advantage to you having phone conversations with her ahead of time spending some time to get to know her and for her to know you. If you're friends then you can talk about what you want and don't want.
Do not dwell on her history. She has no history with you. Suspend judgment until you give yourselves a chance to get to know each other. Many years has passed since those things have happened. You said, she's married now and more stable. Expect good things from her until she shows that she can't be trusted. Often, when we expect bad behavior, we get it because the way we treat the other person makes it difficult for them to be good.
You will only have drama if you allow it in your home. You and your husband decide on what you will accept and ask people to leave if things start to get out of hand. Treat them with kindness and respect while having boundaries and planning a way to enforce your boundaries.
I suggest that you may be quite surprised to find that when you are open and accepting that she will be too. No need to build up a wall before you know it's even needed. Most times, when we treat others respectfully they treat us respectfully. If they don't then it's time to do something differently.