I wouldn't worry too much about your wife criticizing your family. I don't claim to have even the slightest knowledge of the female mind, but my mother did it quite a bit with my father as well. I think it is some psychological thing where she is self conscious or self righteous about of her own family, while also in a backwards way complimenting you on how well you turned out with such a difficult family. What do we know though, we are men and our minds don't work like that.
I was home schooled in a way that you describe, and I think I turned out alright. However, I played a lot of sports, began working at 13 years old, and had brothers to hang out with. I could see why your wife would be putting your kids through a bunch of activities. A lot of home schooled folks that I knew were really socially awkward, making them difficult to be around. If you have girls, I don't have any advice for you, because I only grew up with brothers. If you have boys and begin teaching them only at home, make sure you get them into sports or something to get them around other kids, otherwise they might end up awkward and effeminate. That's just what I've experienced, but I'm not a father yet, so take it with a grain of salt.
Good luck and God bless.