I wonder how she'd feel if the shoe were on the other foot, and you were the one occasionally sleeping at home, and sometimes somewhere else? Then, not acknowledging her presence at social functions?
I doubt if she would tolerate it, but then you seem to have a stronger moral compass, so it is what it is. I agree that your W is being disrespectful of you, the M, and herself, but she obviously doesn't see it that way. From my perspective, I think she sees it as her asserting her independence. Only you will know how long to persevere. I lasted about 9 months before I asked for a D, but it never got that far, ultimately. But, my H acted in a completely different way, so there really is no comparison.
Take care, CL.
Me:57 H:52 M:28 Got another lawyer last year and filed. D35,S/D twins28,D22 EA4/04 End? Who knows? "Life is like a mirror. Smile at it and it smiles back at you." — Peace Pilgrim