HMH, you are low because not only did your H betray you, but he is now doing it under your nose.
If he insists on staying in your home, then sorry, but he can't go off and screw the OW and come back to the family home.
Right now he has it all, a bed to stay in, a family and a mistress. He literally can not have his cake and eat it. He will never, ever leave under this arrangement, why would he?
This is mental cruelty. It is abuse. You can and MUST protect yourself from him and his affair.
If you tell him that he can't see her while he lives in your home. If he wants to see her, that is fine, she is welcome to him, but he has to go.
That is then the ultimatum.
The next time he then pisses off to her, you sling his stuff out and bolt the door. You call him on the phone and tell him not to bother coming back, precisely because you gave him a choice and he took it. Consequences.
He has a right to a proportion of the houses value, but he doesn't have a right to inflict his cheating presence on you.
Something has to give. When he has gone, you won't have that sick feeling when you hear him come in.