Re: DD has a "secret mommy"
This might not be something you want to hear, but maybe she wants to call the GF mommy? Maybe she asked and they thought it would hurt her feelings to tell her she couldn't. This might not be the case exactly, but I don't know any 4 year old who can be coerced into calling another woman mommy and then be happy about it later. It sounds like she doesn't have a problem with it.
If I were you I would be hurt, and probably upset. But maybe your daughter has grown to love this woman and sees her as the mommy of her other home. If she's made a good bond and feels comfortable there then that is a positive thing.
That said, secrets are not okay. I wouldn't get upset about the mommy thing, but I would tell the ex and his GF that when adults teach a child to keep secrets they are making them easy prey for abusers and predators. A child should never ever be asked to keep a secret for an adult, and they should be taught that someone who tells them otherwise is a dangerous person. They need to immediately talk to her and explain that adults and children do NOT get to have secrets.
Happy atheist in a home full of love