Originally Posted by KalFour
When you say he's abusive, what do you mean exactly? Did he beat her or just yell at her? We need a bigger picture here. Also, his sexual acts on a child were when he was 16 - practically a child himself in many ways. And how old was the child in question? You don't need to answer these questions, just think about them and try to be certain about this man.
As for his rights, you'd be able to take him to court and claim custody of the child, or even revoke his right to see her if you could indicate that he would endanger her.
All the same, if he rarely sees her, it's unlikely that he would be interested in taking custody of his daughter ever, so it probably isn't something that you need overly be concerned with.
Hope all is well,
Kal