Stepmom problems

So am a stepmom to a 2yr old baby girl me & her father are engaged we been together since she was 10 months my Fiancé is a great father we have his daughter one week with us & one week with her mom now am having issues because the baby girl call her mom by her name & she calls me mommy i haven't said to the baby girl to call me mommy she just does her mom is trying to say that is us teaching the little girl to her bu her name & not mommy which i find riduculous why would we need to do that for!? When the little girl is with us she doesnt ask about her mom or wants to talk to her on the phone but when she is with her all the little girl do is ask for her dad 
She loves staying with us by the way am the one that sends her pics from my Fiancé phone to her so she can see her daughter oh and everytime me & my Fiancé go out she be writing him oh they told me u was here doing this and that like she be all over our bussines 
End of Rant