The problem is that FB had a pre-planned confrontation and didn't give either of them much space for things to go better. (FB, I wonder if such pre-planned tantrums are an old thing or a new thing?) Now, it wouldn't matter if she didn't want to reconcile, but she does. I agree it is a good thing to set boundaries, take a stand, and not accept unacceptable behavior. But there are more productive ways to do it.
FB, how about:
H: I lost a friend today.
You: I think you mean BFF? It must be hard and painful to lose someone who was so important to you, who you felt saw you and cared. I can see how it would be hard for her too. You've both made emotional investments and it hurts when a relationship ends. I'm so sorry you both have that kind of loss to grieve.
H: I really miss you and the kids.
You: We miss you too.
H: I don't know what to do.
You: That is really up to you. Whatever you choose has to be what YOU want. We'd love for you to be home. I'd love for you to be home. I want a chance to have a passionate, vibrant, healthy M with you. There are ways we can make space for that to happen, but it will involve painful choices for you no matter what happens. I want you to know that is really OK to try with me and change your mind later. That won't make you a bad guy in my mind. But for me, right now, it is not OK to continue to be with you while she's still involved. It's just not what I'm looking for in my life no matter how much I love you.
H: I don't know what you expect me to do.
You: Whatever you do needs to come from you. Treat yourself well. Respect yourself, be compassionate toward yourself. That's what matters the most.