If she doesn't play nice (and clearly she doesn't) then you already have plans.
Looking out for you and having fun with your D esp when you have plans, trumps "mommy time" (and is not selfish). Btw, since it's your day, what is so ab fab that it needs to change your plans? Yes, I would ask.
Mommy time to me is just hangin' out with my D's. sometimes we do something special, but more often than not the really "special" stuff happens when you least expect it.
Ok, I got my paint brushes. Anybody can play, after all, can you say Jackson Pollock???
Now, we just need an in at a museum or gallery......hmmm
put your three sided coin away. It doesn't matter what she thinks about you. If you have plans, and you do, tell her that. She has the next weekend to have girl time doesn't she? Or her evenings...
Wait - what do I know?! Ignore me. (but remember I'm right a lot...)
....Understand, that I can't, not be what I am I'm not the milk, and Cheerios in your spoon ~ Avril Lavigne ~ ..."Nobody's Fool"...
Grace, I took a few art classes in college, can I play?
T, your day, your plans - you decide. Mommytime is no more important than daddytime. She can have all the "special" time she wants on her days. Go with your gut.