And what would I do about the problem of unwanted pregnancy?
First of all, I would mandate comprehensive sex education for every 9th grader...a program which gave students the knowledge and skills they need to postpone intercourse for some years and be safe and healthy when they do engage in it. Just like we all have a disaster plan for a terrorist attack we're likely to never need, so 9th graders need to know about all forms of birth control (including the fairly effective type approved by the Catholic Church). Included in that sex education would be symptoms of pregnancy and the importance of confirming a pregnancy quickly when one misses a period. We have every reason to believe that this alone would eliminate half of the unwanted pregnancies and abortions performed in this country.
Secondly I would balance society's interest in protecting human life with society's interest in protecting human freedom in something like the following way: An unwillingly pregnant woman can obtain an abortion up through the 12th week of pregnancy without giving a reason. Abortions would be performed on minors but their parents would be notified. Girls who feared abuse by parents would be offered the safety that all youth who fear abuse are offered. (which is not much, I realize, but there is no reason to give sexually active girls more protection from their parents than non-sexually active girls get.) The parents could not countermand the girl's decision to abort but could attempt to influence her decision. Between the 12th week of pregnancy and the age of viability (a changing target), a woman could only obtain an abortion by showing that the circumstances which caused her to initially accept her pregnancy had changed. (ie, a change in her health or serious fetal defects). After the age of viability, abortions could only be obtained in the most serious of circumstances; the discovery that the fetus is doing inalterable damage to the mother's health or is itself doomed to death or intractable pain. In other words; a woman has the right to decline to carry a fetus, but this right must be exercised within two months of her becoming pregnant, except in unusual and tragic circumstances.
One final note, In my opinion, the right to abortion is the right to decline to support an uninvited intruder in one's body. It is not the right to "do whatever one likes with one's body," which is absurd. This way of formulating the right to abortion has two implications. First of all, the right to abortion is the right to remove the intruder, not the right to kill. At this point in technology, that removal results in death, of course, and this is not to be glossed over. When the time comes that it is possible to save the lives of very young fetuses with fetal transplants to a willing donor, for instance, or to an artificial womb, I believe that the woman having an abortion must opt for those solutions. Secondly, I believe that it is cavalier to the point of immoral to deliberately conceive a new life and then discard it because it does not conform to exacting standards such as desired sex, blood type to give a family member a donation, just to name two current possibilities. I know of no way to make abortions of "disappointing" fetuses illegal without making all abortions illegal. This is where the moral force of churches and society must be exercised.