There is no data that shows private education is better than public. Because the regulations on charter and private schools are so much more lax, you are absolutely correct to fear the material and the staff of those institutions.

Private schools aritifically boost their numbers by expelling students that are difficult to teach. This results in high performing students getting a sub-par private education while struggling students are dumped back into the public system years behind where they should be.

The only people that benefit from charter and private schools are people who hate actual education and people who make money from private education.