Have you been in touch with the straight spouse network? That has been a lifesaver for me. My ex husband is gay. He also tried to prove me unfit. My life has been a trainwreck due to the demands placed on me by him. Happily, with kids now older, and everyone learning how to establish their personal boundaries, we are getting free of this. But it is never amicable for us. My ex is in the closet. Part of the way he tried to prove me unfit was by ridiculing me for knowing that he is gay.
Please PM me if you want to talk further. When your wife goes with another woman, men go through distinct stages of grief. Also, as cooperative as you want to be, somehow you always wind up feeling like some kind of villian, even though you may be the stable and consistent one.
Many men I have met through the
straight spouse network have achieved constructive resolutions to custody issues - not ideal resolutions, but constructive enough to maintain custody and involvement while getting past this trouble. Some do have full time residential custody as well.
I suspect from your posts that you may have questions that so many men in this position have faced. Peer support really helps to put it in perspective, and it is very confidential.