Well even if the OP's wife (ex-wife) is brainwashing their daughter, that doesn't mean that the OP automatically gets to take away his daughter's sense of self-worth and inner power and the will to choose. If she is being brainwashed, she'll figure it out. But she's a young child right now. She is vulnerable to every adult she comes into contact with as a young child.

It sounds like you're telling the OP to go ahead and take control just because his daughter is young. Being young doesn't negate her right to choose. If the OP takes away his daughter's power to choose, just because she is a child, he's setting up a toxic dynamic between them where he calls all the shots and becomes a controlling, abusive presence, and the daughter learns by conditioning that men have all the power and she has none because she is a female.