BSC!
#1, you gotta relax. The tension you carry (I am so anxious and scared to go home today.) is not invisible. you have to not pretend to be relaxed. Really relax. She will respond to you if you are much more relaxed. No pretending!

#2. if she wants to come back to the room, that is her initiating a move back toward you. Something I don't get: why would she want to come back if NOT to work on you together? Or are you saying, if she comes back you have some specific requests - like she needs to agree to counseling and x and y and z?

If it were me I wouldn't put the bar up too high. if she came back to the room, I would take it as a big positive step. Then the next morning I might ask (gently gently) - "how'd you sleep? I'm glad you're here."

Then maybe after a few days of "how'd you sleep", if there is an opening you might broach the subject of going back to counselign. but I am way ahead of myself because I don't even know if that is your issue or concern.

bottom line it would be a strong positive step, something very hard for her to do, - coming back to the bedroom I mean - and I would want to recognize and support that.

#3. should you have sex if she approaches?

This is an easy one. If she initiates, then yes.