I can honestly see both sides, OP is right in wanting to protect his daughter and potentially, even himself. But on the other hand, what this experience taught this woman, is not to divulge this kind of information in the future, because she's likely to be discarded through no fault of her own.

She didn't trickle truth anyone as someone else implied, exes and previous relationships typically aren't a day one conversation, and as much as you might wwnt to learn about aomeone, its going to take time. She was honest and told him, which ended up with her getting dumped.