Homeschooling can only work where two parents are very committed and capable. When you can't teach someone how to tie their shoes h.s. cannot work.
I think unless you are an amazing teacher and patient person private school is vastly better than home schooling.
I know this is going to get me a shit storm, but home schooling is probably the worst way to educate a child. If you have a crappy school public school send them to private. Most home schooled kids end up in a public highschool because their mom's can't teach them Chemistry, Physics, US History, Calculus etc etc, and when they do its a disaster. The kids are terrible at socializing, and are usually werid. There were two home schooled girls at my Highschool and they were not right socially.