Boyfriends baby mama is not close to warming up to me after 4 years

My boyfriend and I have been together for over 4 years and he has a daughter with another gal. She is 5 years old (just turned) and is an amazing and wonderful person, who I adore. I’ve been in her life long enough to have a very health, and fun relationship with her. Her mom seems to hate me for even being in her life though. I try so hard to always put his daughter first and do what’s best for her and treat her like she is my own child. Heck I love her like she is mine! However the more I try to do right by her the more drama it seems to cause between my boyfriend and his x. It’s been a hard struggle for us and I fight the urge to be petty and want to hurt his x when she is rude, selfish, controlling, shallow and a total B to him or myself. I kept telling myself if I stay above it all and just keep loving his daughter and trying to do what right it would all work out. Well… it’s been a few years and NOTHING has worked out!! Can anyone give me advice on how to handle the situation with her?! I’m so sick of turning the other cheek as she insults, me and try’s to get rid of me, and bypasses me after I’ve asked her to communicate with me! I’m polite and try to have good honest communication with her and all she can do is lie to me and then through screaming cussing fits in front of her sweet girl to my boyfriend when I’m not there and it breaks my heart! Selfishly it hurts because some days his daughter wants to be at her moms and I have to bite my tongue and say “you get to see her tomorrow!” when what I want to say is horrid and mean but I don’t think her mom does the same! Do I just keep on trying to be the nice mature one?? Is it okay for me to lay down the line with his x? Does he need to be the one to do it?? He is scared of her crazy fits and exhausting drama so he won’t! But then that means he never stands up for me because he doesn’t want drama. Is that smart of him or lame of him? Should I have a problem with the fact that he won’t stand up for me to her, or understand the fact that he is trying to keep everything as calm as possible for his daughters sake? Help! 💔