You want to erase her experience. Okay.
There's a very easy way to take underage women, rape and incest victims, obviously medically unviable pregnancies, and women with severe health problems out of the politics of the abortion discussion:
Provide common-sense exceptions for such situations.
It's that easy!
Unwilling to do that? Then reproductive care advocates will absolutely use them as a political hammer, and they'd be right to. If you want to craft laws that punish "s**ts" and you end up sweeping up 10-year-old rape victims in your dragnet of moral policing, then yeah, that's a problem.
A more subtle point is that reproductive care access for these "special" cases (the kinds of abortions that almost anyone can agree are understandable) depends to a great degree upon access for "routine" cases (the kinds of abortions you want to police and hate).
We can have that argument at a later date once your party works through its other crap.