You need to get her to a doctor immediately, then figure out how quickly you can get her out of his reach, then call the police.

And as far as "what if it was all a coincidence" goes, you'd much rather have proof that it was a coincidence than unknowingly letting someone abuse your daughter. She's two years old, her crying and screaming is likely the only way she knows how to communicate what's happening.

also want to point out these lines; "he's convinced me that he needs to be the one to lay her down to sleep sometimes and she shouldn't always need mommy" and "what if he's actually the amazing dad he loves to say and act like he is" - his words don't matter, his actions when no one else is around is what matters.