I think it is absolutely appalling that your WW appears to be saying that your not really her father. As a step-father, I recognize what it means to accept a child as your own, to love them, care for them and give them a father's love, discipline and lessons that they would otherwise not receive. You adopted her, she is your child as much as your WW's, and there is nothing your WW can do to change that.
With that said, this is not a battle that you should go into with the mindset of "I must win this". Keep your daughters best interest as the reason for each decision you make.
In no way and I'm saying your not her best interest, and understanding the WW mindset, the best thing for her may be more time with you, but I don't know the real life nuances of her R with your Daughter.
M - 9 1/2 years 5/5/16 - Bomb drop - 3 week EA 10/31/16 - We sold house 01/10/18 - D Finalized