OW's H IS her daddy, as far as she's concerned. To that little child, your H is just some family friend who takes her out sometimes - OW's H is the man who was her father figure, and is the father to her siblings.
I understand your H's desire to parent his only child. Just try to remember that what HE wants and what is in the best interest of the CHILD, may not always be one and the same. She is not a possession to be fought over.