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.
The principle here is that individuals in our society do not have an obligation to give of their bodily resources to help others survive, especially when they bear no responsibility whatsoever for the predicament of the person in trouble. This principle has been pretty consistently applied and respected in American law and tradition. It's the reason there is no forced organ or blood donation and women aren't forced to carry unused lab embryos to term.
In the case of a rape pregnancy, it seems to me that the victimized woman seeking an abortion has a very strong case. She had nothing at all to do with the creation of the embryo she now carries, so shouldn't this principle apply to her? Isn't she justified in seeking to end the violation of her rights? The only way for her to cease the use of her body by the embryo is to have an abortion. The innocence of the baby is not relevant in this scenario, just as the innocence of unused embryos is not relevant to their situation.