What to do

This is about my fiancé’s dads girlfriend. Okay to start off she is very controlling. She makes it clear to my step daughter she doesn’t like me. She tries her hardest to make things all about her. We are having our little boy in about a month. She told me she doesn’t want my step daughter to call me mom because she doesn’t see me staying around very long 🙄 I laughed in her face knowing I was pregnant. I made it clear when we announced that if she doesn’t want to have a relationship with me a healthy one then she can’t be around my child... she will definitely NOT be called grandma. Am I wrong?

I also think she’s jealous that I’ll be having the family’s last name and he doesn’t plan on marrying her.