You also need support. You love your FIL and he is family to you. Does DH acknowledge this?
The next few months will be tough. You need to reflect, as pp said, on what you want and need. That will include being a support to DH and FIL but also being with all the family, for your own sake.
So this reflective mode might help. Give yourself credit, don't blame it on perimenopause/"over" emotion/yourself.
He seems to be close with this woman and that's damaging your marriage. You've made this clear to him.
He's making the choice to continue with her.
He's then turning it on you by saying your marriage is over if you continue to be sad about his deep friendship which is affecting your marriage.
I think be with the family, be with FIL. Reflect. Maybe take some time to truly consider the relationship and your own mental health - maybe with a counsellor? Create a little emotional distance, a safety zone for yourself. I don't think your H will make any changes or offer reassurance at this time.
In this time you may see more of what you think is happening, he's detaching from you. This might continue to pain you or become more acceptable. Something else may develop, your relationship might strengthen, it may fade because of other reasons.
Give yourself time. Be kind and present with FIL and family. I would say one time in a short serious conversation to DH that this friendship impacts your relationship and he seems to be distant but that at this time the family is priority and you're part of it, so there needs not be discussion about this friend and that you're there for him. You don't have to say any more than that.
I'm sorry you're going through this OP.