The problem with this kind of argument is that pro lifers don't see the abortion argument in these terms. Nobody on the right is going "Yes crush women's rights woohoo", they see it as almost murder.
Vehement opposition to abortion is strongly correlated with wanting to control women on other levels. While the right tries to frame the abortion issue as the right to life of the fetus, given their lack of respect for other women's rights/human rights issues, it is likely that the right tries to hide their anti-woman desires, to claim to be pro-fetus rather than anti-woman.
In other words, assume the worst about your political opponents. I'm sure there are some pro-lifers who just really hate women and want to punish them, but my experience with them indicates to me that this notion of "pro-life being anti-woman" is broadly speaking a left-wing fiction.
Yes. Especially as polling suggests that women aren't particularly more likely to be pro-choice than men. And I don't think internalised misogyny can explain it away.