First, I was trying to give you suggestions that may help you in your personal situation.
Secondly, I am confused as to what you think should be done. Because it appears that you do not like paying a lot of tax money but expect there to be affordable quality education available?
I mean, if you want more educational options available in your area then presumably that means the government at some level (local, county, state, federal) would have to pay for it which means an increase in taxes (for someone at least).
Third, you did say "Low-income families have a higher probability of raising children in a dysfunctional home who then become a burden on the local school district. " So it seems fair to suggest that you should consider raising the level of your income to meet your desired needs.
Fourth, in all fairness I don't have children so I am not sure why I should have to pay any tax what-so-ever for your child to receive a poor education.