Is it ok for my step-daughter to call me mommy?

My husband and his ex broke up when my step-daughter was about 1 and we started dating shortly after they broke up. They went to court and my husband is the custodial parent, his ex is supposed to have visitation every other weekend(she disappeared for a few months and skips weekends). I moved in with the two of them, we got married, and recently had a baby! We always taught my step-daughter to call me by my first name, but she started calling me mommy when she was about 2. Her biological mother was really angry about this, how do you explain to a 2 year old what a step mom is, or what a husband and wife are? So I did the best I could, I told her (showing her a picture of her mom) that she grew in her belly.. the same way her baby sister grew in my belly, and even though she didn't grow in my belly I love her just the same. She is now 3, and if you ask her who her mommy is, she will say her biological mothers first name, and if you ask her who I am, she will say i'm her step-mom, but she still calls me mommy.. this makes her mother furious and she says all we are doing is confusing her by letting her call me mommy, and when I tell my step-daughter she can call me by my first name she says, "no, I want to call you mommy". My husband thinks she should be able to call me mommy, but her biological mom says we need to cut it out. I would be mad too if my daughter was calling someone else mommy so I understand why she is mad but I don't know what she expects because she really doesn't see her that often for one reason or another. I really think if she saw her on a regular basis, my step-daughter would have never even started calling me mommy. I don't mind her calling me mommy, I am a stay at home mom and I take care of her no less than 24 days of the month! She wants to go to court so someone can tell my husband he is wrong for letting her call me mommy..?