Verified answer

If the parent sees their daughter every other weekend then they still have custody. They don't have primary custody or legal custody but they still have their parental custody which means they absolutely press charges of statutory rape against the boyfriend. Actually it doesn't matter who presses the charges. If a teacher or a grandparent or even a neighbor has proof of illegal activity (pregnancy is pretty strong proof) then they can go to the police and file a report. But it depends on the age of consent in your state. If she is underage then there is a good chance someone is going to press charges. If it was my child, or even just a child I knew I absolutely would be notifying the authorities.

Can a parent with no custody press charges

Need more info. Laws differ between counties and even state/provinces.