I am not speaking (or typing in this case) from the views of an expert in family law matters but rather from my own experience.
Worriedmommy, I know exactly how you feel as I wore your your shoes almost 3 years ago. Without going into a lot of details, my ex and I were locked in a lengthy and costly legal custody matter over our then 7 year old daughter. Like your ex, he encouraged our daughter to refer to his then girlfriend as "mommy." Furious, I shot off an email to my attorney asking her to demand an order from the judge prohibiting the ex from such behavior. Against her (attorney) better judgement, my concern was addressed in court and the judge literally scolded me for my pettiness and advised me to focus on the relevant matters at hand. He also reminded me that this matter is not about my feelings or desires but rather the best interest of the child. The judge saw absolutely no problem with it due to the increasing number of blended families. Was I upset? You betcha! Was there anything that I could do to prevent my daughter from calling another female "mommy?" No.
Like your ex, my ex also spoke horribly about me to anyone who was willing to listen. I was a full-time single working mother who did not have time to worry or care about what others thought of me. Those in my small network knows me and would give me the benefit of a doubt at the very least. I will confess as I pretty much did the same. Not to the ex's extremes but that's irrelevant. Upon realization of how much I was hurting my daughter when I spoke negatively about her father in her presence, I ceased. I would only imagine that your daughter must feel the same when she hears anyone bad-mouthing her mother.
The ex went M.I.A. shortly after the judge issued an order that wasn't precisely what he wanted. During his absence I had the opportunity to reassess myself and the situation -- the good and bad. It was also during this time that I found the "serenity prayer" (please google it if you are not familiar with it) although I am not religious by any means.
Now fast forward to almost 3 years later... My ex just recently started spending time with our daughter again. He has not changed; he wants our daughter to refer to his new girlfriend as "mom." My daughter aims to please and she inherited my negotiation skills so she refers to dad's new girlfriend as "<insert name here> Mommy." I no longer have issues with daughter calling another my "title." I take comfort in knowing my place in my daughter's heart. My daughter is highly intuitive and she is aware of the sacrifices I have made so that she will not need to sacrifice. In summary, I know I can not and will not be replaced, even long after my time on this earth expires. Some kids do not have a mom nor a dad; I am very grateful that my daughter has another "mom" who loves and take care of her in my absence (while she's with her father).
Worriedmommy, I know how upset and hurt you are...believe me, I truly do. You would be amazed at how intelligent kids are these days and I'm certain that your daughter knows who gave birth to her. I hope you'll find comfort and peace one day as I have and I wish you all the best.