Hello and welcome. I am sorry for what brings you here, but glad you are here.
I say this gently. You are not the one who has to fight, it would be him, and it sounds like he is not willing to make that effort. Its sad, it's frustrating, it's awful to watch someone you love go down the rabbit hole. If it were just alcohol it would be bad enough, but that he is with another woman? Unacceptable.
You are your kids are worth so much more. I encourage you to seek out Alanon or Celebrate Recovery so you have some face to face support for yourself in supplement to this forum.
Keep posting, you are not alone.