Seeking MC experience

My WH and I have a Gottman trained MC. She also specializes in betrayal. We have done the first session together, and both individual sessions. Our MC wanted another introductory session w/ the both of us, but since I had surgery coming up we went into the individual sessions. Our next session is next week.

Affair summary:

Dday was in March 2026, however, his EA/PA was on/off from 2024-2026. I confronted him twice about the affair in 2024. He lied about the extent of the affair. He did end it for about 6 months and restarted it. I was led to believe it was one meeting in 2024. However, in 2026, I found out it was a full blown EA/PA. He has never had a PA. There were other ruptures by him in our marriage w/ inappropriate 1 on 1 time and communication w/ other women and poor boundaries. He has owned that he has caused me trauma, however, he is at a loss in inner work. He has only done 4 sessions of IC due to schedule. I hav attending 20 sessions w/ many rounds of brutal EMDR.

My WH has been burned out with reconciliation and disconnected from me since the end of June. There are moments of connection, but it fades. My husband keeps floating coparenting ideas and a separation where he would sleep in a nearby apartment for space, but still be at our home often. (We have a beautiful 7 year old who is active in Jiu Jitsu x4 a week.)

My WH has continuously told me that he has minimal energy to spend on reconciliation or diving into his chronic cheating behavior. He even told me if he has to support me, it empties his cup for himself. I realize now after 11 years together that his emotional capacity is far smaller than mine.

He said he is refusing to do any extra work when in comes to reconciliation besides MC once a week (if he's not traveling for work) and IC, which happens to be monthly and whatever the counselors assign as homework. I know his IC is too infrequent to make progress. Any time I say or push about the matter he gets upset.

Is there a chance our MC may ask my WH to essentially get real w/ himself if he wants reconciliation? I still do but my husband is wrapped up in solipsistic shame.