I was homeschooled from 4th Grade to 6th Grade and from 9th Grade to 10th Grade. I was much smarter than my peers, so as a result, my teachers were pissed that I was ahead of the other students and tried to put me in special ed. My parents knew what was up and just took me out and put me in an online school. Then when I was in 11th Grade they enrolled me in a collegiate high school program.
The thing is, homeschool parents always say "I'm going to put them in programs where they can interact with other children," but the thing is, it is not the same as them having to deal with other children their age for 8 hours a day. I love my parents, and I understand they were doing what they felt was best for me, but they did harm me socially.
When I went into the 11th Grade I was unprepared and I had issues adjusting, and as a result I struggled academically. I wasn't bullied or picked on or anything, but I was frustrated because I was socially awkward and I knew it.
By the time I entered the 12th Grade, I learned the game and I was able to catch up to my peers quickly. At the same time though, I had really only that year to socialize and do immature teenager shyt before I went off to college. Even now, in college, I'm still immature in a lot of ways. Other college students had 12 years to do dumb shyt and charge it to the game. I only had 8, so as a result, I do a lot of dumb immature shyt.
Basically what I'm saying is, you will have to sacrifice doing one or the other. Either keep them in public schools, and let them learn a bunch of bullshyt and get put in special ed if they don't conform like the other kids. Or you can take them out and homeschool them, and ruin their social life and pray to God that they will be able to adjust when they enter college.
Oh, and from Kindergarten to 3rd Grade I went to a Montessori. It's similar to a private school. Mine was run by a bunch of muslims and it was great. I'd suggest enrolling your kids in a Montessori. The only reason they didn't keep me in the Montessori was because we had to move. It wasn't too expensive, the teachers were great, and there was a lot of chance to socialize.