If it is just your own PTO...I'm pretty sure they have to compensate you for that earned PTO. If this paid parental leave is simply paid by the company and was offered as a benefit, the only thing I would say is that you should only take the leave for as long as you are not working at the new company. To me that seems like the right thing to do from an ethical standpoint.

This is more true if it is part of FMLA leave, and the government is paying for part of that leave.

If it were me and I had this second opportunity, I would first see if my new start date could be at the end of the leave. Then I would when there is two weeks left on the parental leave i would give notice.