Chaim, I think you are doing the right thing, you are just complaining about it.
“choosing” not to work and rely on others paying for you is not an erliche option.
If you think working in business is better … Not exact match, but there was shochet who told R Salanter that he doesn’t want to be responsible for aveiros in shechita, so he is going into business! R Salanter was horrified that he is not afraid of aveiros in business .. accounting is not shechita, but the business alternative is still the same. Not randomly, you bring the “nursing home” example – a business rife with people being in trouble with medicaid, hiring illegals, profits balancing how much you spend on feeding elderly … I would rather be an accountant for Enron that face this yetzer hara.
So, just stop thinking that the grass is greener somewhere else, you are doing well.
I would look at adjustments – 401k, vacations, camps – really, train your kids and learn yourself to enjoy interacting with them. If the choice is not being to pay for school, camp should go first (my school has question “which camp you go to” in there where they are trying to figure out how rich you are).
If kids are too young for kiruv camps, they can help out in a local summer day camp with little kids. Mine started doing it, I think, when they were 12.
Maybe assist at a local chabad house, if you have one or maybe your place is too frum.
In terms of school costs, I am big proponent of doing general subjects in online schools from about 7-8th grades – you can then have all kids together in Jewish classes, and everyone can go there own way in general studies – some might want Yinglish only, some might want AP and SAT. And this cuts cost at school. If you are really pressed – experiment with 1-2 (better 2 close in age) kids in fully online Jewish schools for a year.