Ex husband/gf ...and my kids.

I have a 5 year old son and a 7 year old daughter. We have been divorced for almost 4 years. He’s been with his gf since before we broke up (my so called friend...) we share 50/50 custody at this point which I’m trying to change for multiple reasons....he’s my thing. They make my kids call her “mama..” I have a serious problem with this. She is not their mother....they are 5 and 7 they are being forced to call her this. I told my ex this is not ok with me at all. He told me it’s a “ nick name” and it’s not a big deal. He also told my kids “mommy doesn’t like it, so just don’t tell her you call her that” so is this something I can use in court? I feel like it is.