WW here...I think you have every right to ask for these things as a condition of R and your WH needs to understand its what he needs to do if he also wants to R.
He may not like it but it is a consequence of his actions. Explain to him that these are things that will help you regain your trust in him and make him a safe person.
IMO (and personal experience)it is hard to R while you are separated. My BH discovered my A last December and we were separated from the beginning of January until August....while we were separated I was in IC,and also still very much involved in an EA with my AP.....once I wasn't living at home it became that much easier to continue a relationship with him.
I am not trying to scare you or put doubt in your mind, but am merely trying to illustrate that even though on the surface I was trying to R I was still in my A.
During this time I was pushing my BH to let me come back home....he hesitated (I didn't realize it at the time but he knew I was still talking to AP)
I don't know what changed his mind, but my BH finally decided to let me come back, which is when I decided to really go NC with the AP. The whole situation exploded then and I have since been NC with my XAP and fully committed to R.
I'm sorry for the rambling story...like I said I just wanted to point out its hard to R if your living two separate lives.
Your BH May not like your conditions but if he wants to fix it he will realize he needs to do what you ask. And you as the BW have every right to ask for them.