All I can saw is wow...sounds like some good/some ehhh - just getting some movement and it is shaking things up.
I agree that it is weird of her to take a "friend" to the movies with D. My take on it, she's into him and something is going on or he's into her and trying to be the rebound guy. I think you're going to have to let his being around go. (I wouldn't - you know from my posts that I would move out of state before that whore OW spent time with my babies - I'd also probably do a little worse too and I like to think of myself as a nice person ) Do what you can, you cannot control him being around, but you can try to control your reaction.
Csreful with teh MIL, because at the end of the day, W is family...PLUS my MIL has shared info with others that I wish she hadn't AND has at times put me in the position of comforting her (there's a level of selfishness in that, they cannot get through to their child, but you're present and sane and etc). It gets very difficult...not that any of this is easy.
You're right not to lower the bar - W has a long way to go. It's nice to know that MIL thinks she is close to bottom. I read something today though, it said "W has come to terms with the idea of a Divorce/end of relationship as their next step. In order to save the relationship, W must now DIVORCE mentally from their decision to end the relationship. This is an equally larger decision."
I don't know how you draw lines about him being w/D. My H knew OW would NOT be ok, but she really is a messed up person, so it was easier to agree on. Your W knows what she is doing is wrong. Keep trying to be the more attractive, elusive option. A fight or deep talk every now and then is ok, I think. You just have to come back from it. It means you both still care enough to put in effort, pour out some emotion. Now makeup, make nice for D's sake, but don't give too much ground. Your wife teaching your D that it is ok to lie and sneak around behind your back is going to bite everyone in the A@@ in a few years. Your wife needs to understand that you are not mad that she's dating or whatever with her friend.
The issue is that she is undermining your authority as a parent, setting a bad example for your D by encouraging her to lie/cover for her mother (your perception of how D sees this, let's assume that was not wife's intent), and that you are disappointed that she felt the need to change the focus of mother/daughter time to include someone else (making D uncomfortable, not giving her more time to adjust to this before bringing other men into her life). As a woman and a mother, that speaks to me.
Faith is, at one and the same time, absolutely necessary and altogether impossible. --Stanislaw Lem