I am a second wife. For what it's worth, I had no interest in replacing my s'kids mom. If I were able, I would like to be friend - like with her, but for the time being, that's not possible either. To point out - the stuff she couldn't/wouldn't do, the kids would ask me to do - if I can say yes, I always do.
I guess what I'm saying is to make everyone more comfortable, I would talk to your ex and his wife to be - let them know that you want very much for the three of you to work together for your daughter's best interest, and ask them to please come up with a 'name' that makes her s'mom comfortable, but is not mom, mommy, or mama. You welcome her in your daughter's life (assume she's going to be permanent - it's easier to get along than to fight, especially for your munchkin), but the mom job is not up for grabs. My stepchildren named me SMOM if that helps you out.
Assuming that gets addressed comfortably, I would suggest that you talk to your ex about how uncomfortable your xmil's comments make you. Especially since they will undoubtedly create insecurity in your daughter's mind. He can address that with his mom.
Finally, realize that sometimes a stepmom isn't a horrible thing. While not taking away from the fact that you are your daughter's mother, we can be the most caring babysitter you'll ever see. I love my stepchildren, hands down, as much as I do the two I gave birth to. I've been known to do field trips when their mom can't, wipe tears when she's not available (or when it's my husband's time with the kids), help with the legal end of parent teacher conferences (it's harder to bully another teacher than it is regular parents). If the ex and I were able to maintain a cordial relationship and she were interested, we could also share the (cost) of parties and larger gifts - but like I said, she's not interested right now.
S.