Planned Parenthood is a great organization, but I think the services are cancer screening, birth control, and women's health care. They may do a little counseling, but I would guess they specialize in a short term variety-- see people, figure out the issue, send you on to someone else. GT is not usually really short term (by short term I mean 3-5 sessions). It's possible that someone there would be sensitive to trans issue (actually I'd guess the odds are higher than some other random group), but figuring out where to send you and so on, I'd guess they wouldn't be able to do this.
I think that perhaps your parents could see the point of sending you to someone who might be able to help you with these issues, even if they don't approve. Why would they spend money on someone you won't go to? I don't think there is any point at all in seeing a non-GT at this point.
It's possible to find someone who gets it, I have a friend with a degree in social work. She knew a lot about this when I told her. But the odds are against it.