Feeling Defeated, Overstepping boundaries

About 8 months ago my kids came home saying their dad was forcing them to call their step-mom “mom” or they would get in trouble if they called her by her first name. Long story short, they still have to call her “Mom.” Their dad and their step mom just had a baby together and they think he wants them to call her mom because the birth of their baby sister. Am I the only one that sees this wrong?!?! We are currently going through custody, I have the kids more of the time and he wants 50/50 custody.

I started writing notes in the kids lunches and then she started leaving them notes and signing them as “mom”!!! This bothers me so much, I have tried to talk to their dad and he doesn’t care that the kids are telling me they are being forced to call her “Mom.” If they call her by her real name, they say he asks them, “what did you just say, that’s not her name.” Or shakes his head until they says Mom instead of her real name.

Any suggestions? They are 8 & 6, they have spoken to their school counselor and told her they only want to call me mom.