Should my stepdaughter call me mom?

i have cared for my step daughter since she was 6 months old and she is now 4. i take her to the doctor,dentist, register her for school, care for her when she's sick, etc. basically all the things her mom should be doing but doesnt. i refer to her as my daughter ( funny thing is that she looks like me) and she started calling me mom when she was 2. recently when she was on the phone with her mom she refered to me as mom and her mom yelled at her and she was in tears. she refers to her mom as mommy tracy. i dont want to tell he rits wrong to call me mom because she gets sad and i have a son who calls me mom. i feel like she thinks im disowning her when i tell her not to call me mom, but i dont like it either when she gets yelled at for calling me so. everyone, including my family has a problem with her calling me mom except my husband and i. most outside people ( teachers, docs, etc.) never even met her mom and think of me as her mom. what should we do?