It might help you manage your feelings if you understood that she isn’t telling people lies. Sometimes she is telling them her fears. Sometimes she is telling people what she thinks they want to hear so they will love her. She is only 6 and she is trying to figure out her place in two complicated families. She is the only child going back and forth. Her half siblings each get to stay with one set of parents. Foster kids came and then, mysteriously to her, went. Does that mean she can disappear too? Even her literal “place” in your home is going away. I suspect that underneath the crying and story telling is a very scared little girl. I hope her play therapist has all the facts about the family configuration and your stepdaughter’s place in it. Otherwise, she could easily misinterpret what’s going on here.
I think you and her mom need to sit down with this little girl together and talk with her about her special place as the oldest and as the one kid who gets to have two families. I would clarify for her that the foster kids needed a place to be for awhile but now are back where they belong. And I would make sure that she has a special place at each house that is just hers. (The baby doesn’t need his own room at first. Keep him in with you or put the crib in the hall but don’t displace this child for now. ) Then follow up by making sure that you give her positive attention for being a big girl and a helper. Involve her in getting ready for the baby. Work with her mom so that she doesn’t feel that she has to play the two of you off each other. She needs to know there is room in both households for her to have a valued place. Make sure that each of you (her mom and you) call her each day with family news when she is at the other house so that she doesn’t always feel like everyone knows what is going on except her. Once your stepdaughter is more secure, I’m reasonably sure you’ll see an end to the issues.
I wish you all well.