Hi Zach,
I’m sure someone will be able to give you a more comprehensive answer, but a basic understanding of Catholic ethics/morality is that you may never do evil so that good may come of it. As examples, you can’t attempt IVF (which is evil) so that you can raise a baby in the Catholic faith (which is obviously good). You can’t murder an elderly grandparent (evil) so that they will go to heaven (good). I noticed when I took Ethics in college that a lot of the scenarios we were presented with could be approached faithfully from this perspective. No matter the good outcome you expect, you can never sin to achieve it.
It’s sometimes a gray area. For example, many theologians agree that it is not sinful (i.e., not considered theft in the way that it is condemned by God) for a starving person to take food from someone who has a surplus of food, because the universal destination of goods should have secured enough food for the starving person to begin with, and it was actually the glutonous person who “stole” it from those it rightfully belonged to, the poor.
Regarding the specific question you mentioned (“If you could save 10 children’s lives by letting your own child die, would you do it?” ) it helps to start by analyzing just the action or inaction part, without regard for the consequence. So, in other words, is it right or wrong to let one’s child die? That alone will determine the morality of it. I would say, it depends. In general, I think it would be sinful for a parent who could easily save his or her child’s life to instead let that child die. For example, denying the child food or witholding basic medical treatment from a sick child is very wrong. One of parents’ most basic responsibilities is to protect their children. It would be gross negligence at best for a parent to ignore this responsibility. On the other hand, I could conceive of circumstances in which a parent could ethically let his child die. An example of this would be if the child had a late-stage, progressive cancer and the treatment options available were abrasive and complicated and might only extend the child’s life for a few months. In that case, it might be ethical to let the child die in peace, without taking extreme measures. But you’ll notice that in both cases that I never considered the fact that 10 other children’s lives could be saved by choosing one intervention over the other. In this scenario, I don’t think it’s relevant.
God bless you for grappling with this. I’ve never read the book you proposed, but I have read “Catholic Sexual Ethics” by Lawler, Boyle, and May. It is very good, though perhaps smaller in scope than you would like. I do recommend it if you’re interested in that aspect of Catholic morality.