M.P.
This is not different than shared parenting in which child sleeps half time at each parent's house. She'll get used to it.
It is normal to have a transition time during which she'll be somewhat cranky for a few hours. Try to greet her with some special routine that you have every time. That will help the transitiion.
What do you mean she kinda knows she is mommy? Isn't she her birth mother. If not then you don't have to do this. How long did she live with the 2 yo's and he father if she's not the mother? If baby is not bonded with mommy then she does'nt need to go. I suggest getting an evaluation with a child psychologist/therapist if she's not her birth mother.
I suggest that the fatger talk with his ex about what happens at their house and try to come to an agreement about having similar rules/lives.
And......remember that the father is the only one who can decide. Be careful if you disagree. It can drive a wedge between you.