I’ve been in this situation. For years I harbored resentment for “mistress lady.” But life is long (if you’re lucky) and at a certain point, everyone realizes these resentments are ridiculous.
It’s hard to move past them, though, when there is deception. If you get “mistress lady’s” side of the story it might surprise you. (I was surprised.)
At the end of it all, for me, for my own health and sanity, I had to leave my parents extreme dysfunction to them to work out…and the mistress…and the half brother…and the deception that hurt so many people…none of it was mine. Why should I carry it? Be reactive to it?
Sounds like your dad is happy. Seems like he wants you to be accepting of that and the mistress lady. If you were, it would probably bring you great peace…and it might even help your mother.