Can a parent press charges for their daughter who got pregnant by someone over 18?

Only if she was under the age of consent when they had sex. If she was the parents can report him to the police for statutory rape but it's the state that press the charges which means the parents who reported it can not take it back or influence it. By then it's up to the court. I'm not telling you what to do but also remember that he is the father of your grandchild. To have a father labeled sex offender is not an easy thing to deal with.