The only reason that medical bills and supporting a family are even questions is that he values his family's well being more than he does that of someone who might be helped by charity. Phrasing things in utilitarian terms, he puts a much higher utility on his family than on a random person. As such, he should only donate to charity once he has spent enough money on his family that the utility from doing is, per dollar, so much less that that factor overwhelms the large multiplier that he gives for his family's welfare compared to a random person's. Given his description, he clearly hasn't reached that point yet, so he should spend nothing on charity.
This leaves guilt (or warm fuzzies, which are the flip side) as the only reason to spend anything at all. The rational amount (ignoring questions like "what utility to I get from assuaging my guilt") is zero. Take care of your family, who needs it, and stop feeling guilty for not donating.
Given his description, he clearly hasn't reached that point yet
I'm failing to follow your reasoning at this point. How does his description indicate that?
("A random person" isn't quite the right reference point, by the way. It seems reasonable to hope that a well selected charity will direct help to people who are in distinctly more need than average.)
I'd like to hear from people about a process they use to decide how much to give to charity. Personally, I have very high income, and while we donate significant money in absolute terms, in relative terms the amount is <1% of our post-tax income. It seems to me that it's too little, but I have no moral intuition as to what the right amount is.
I have a good intuition on how to allocate the money, so that's not a problem.
Background: I have a wife and two kids, one with significant health issues (i.e. medical bills - possibly for life), most money we spend goes to private school tuition x 2, the above mentioned medical bills, mortgage, and miscellaneous life expenses. And we max out retirement savings.
If you have some sort of quantitative system where you figure out how much to spend on charity, please share. If you just use vague feelings, and you think there can be no reasonable quantitative system, please tell me that as well.
Update: as suggested in the comments, I'll make it more explicit: please also share how you determine how much to give.