We had the very unhealthy pursuer distancing dynamic in our relationship too. It was always there, and we managed it. Then we went through a very hard time and his natural response to that - to withdraw, seek time alone, look inside himself - and my natural response - to want comfort, to want reassurance, to talk things through, to want physical closeness - threw us into a toxic dynamic that took years to get to a breaking point. I am still working on this and my part in turning it around is not perfect. He has made massive improvements and is much much more caring and empathic towards me now. It is still not perfect and it never will be.
If you are on the distancer side, it is possible that your H has a lot of deep seated resentment and hurt about that. I know I did. I had to either think that there was something wrong with me that he didn't want me, or something wrong with him that he couldn't want me. It was untrue and unhealthy but it was where my head was at, as a person on the receiving end of distancing that felt and looked like rejection but was what I now know is self preservation.
Figuring out what detachment looks like in this dynamic is very very difficult. At this stage, with him being unfaithful to you, dishonest, not wanting to work on the marriage and compelled to live with you, I would give him as much emotional and practical space as you possibly can, and then give him a bit more. Don't disclose your thoughts and feelings. If he asks you, be short and to the point, 'I am finding this very hard, but I am sure I will be okay.' Lean on your friends, but not mutual friends who will feel they have to take sides. Your own girlfriends. When in contact with him or parenting together, be civil and warm. But don't initiate this contact.
It is incredibly hard. I don't think I could have managed in in house separation so not being able to keep your balance in these early intense days is nothing to be ashamed of.
