She then looked at me and said she wants to work on our marriage. She said that she really wants this to work. She mentioned that she can't offer herself to me romantically at this time because she is still angry and is working through that.
THIS, right here, is the fulcrum you need to get this back to, FFH. Your response here needs to be "I understand. And I think you'll find me more than patient on that issue. Now, this is what I need, in order to feel safe in the relationship going forward . . . "
And then you tick off your 3 or 4 or 5 "dealbreakers"/boundaries.
Your wife, it seems to me -- the one who has strayed from the marriage and from her vows recently -- has structured this as "Let me tell you what I WON'T do," (joint MCing, sexual intimacy), but she has it backwards. When a recently-straying spouse wants to return to the marriage to "work on it," it is the BETRAYED spouse who gets to lay out the boundaries -- not the recently-straying spouse!!!
