Sadly, pro-lifers who don't support a rape exception almost never stop for even a moment to consider the fact that the victimized woman is also a person, and may also have important rights that should be weighed in the equation.
After all, the right to life does not trump all other rights in law. If I need a kidney transplant to live, but there is no donor organ available, I will die...because I do not have the right to force you to give me a kidney against your will. My right to life does not trump your right to your bodily integrity, and that's a very good thing. I certainly wouldn't want to live in a country where the reverse was true.
Your analogy is flawed. Nobody is depriving the kidney patient of their life, or right to it, they will simply die in the natural course of events, barring some action that can’t be legally compelled of others.
Putting that aside, I see your point, but it is simply not sufficient to say there are other rights to take into account, and then wash your hands of the matter. There are means for determining which rights take precedence, and if we apply those tests, then the child’s right to life does trump the rights of the parent that could be construed to conflict with it in nearly every circumstance. The only way you can make a logical case to ignore that is if you simply say that the child is not a person, and therefore has no rights.