2 year old calling me mummy

My OH has a daughter who's life I've been in from she was 9 months we have her Friday to Monday every week. We have always referred to me by my name to her and encouraged her to do so. She's gotten better with her speech and has been calling me "mama" which we put down to me being called emma and she couldn't say it proper so today she kept point at pictures we have and I'd say to her "that's Emma, daddy and Charlie" and she was only saying daddy so when we went to the park she kept calling me mummy and the more I said "no I'm emma, mummy is at home" the more she would run after me shouting mummy, cried when I walked over to the gate screaming mummy no, back. I know her mum used to refer to her old partner as daddy to her so I don't know if she's getting her to call her new partner daddy and she's thinking that we're both if that makes sense? I've tried correcting her and I'd feel so uncomfortable if she said it infront of my oh family or her mum because I don't want them to think we have taught her it because I'd never do that to her mother. If I tell her mum she'll flip and say we are learning her to do it and if I don't and she finds out she'll think we are. What will I do?

Yes she says other other names even when her father said "no that's emma not mummy" she started starting "no mummy" I just can't be bothered with the drama if her mother finds out Because she would stop contact over it