question to moms/MIL

I'm engaged to my fiancé and we are really close with his side of the family! I love them as my own. My mom is/was an alcoholic (idk if she still is) and for many other reasons we rarely talk and are not close at all anymore. I've been thinking a lot and I want to call my mother in law mom instead of Sara. She's the closest thing I've had to a mother/mother figure since I was very young and my mom wasn't an alcoholic. Is that weird? How could I bring this up to her? And how would you feel about your daughter in law calling you mom?