Luckily Horton, you have two misconceptions about homeschooling.
1) You don't have to do the direct teaching. You are more like the Manager, lining up a team of providers. If there is a local University you may be able to register for a course there, or perhaps at the local community college. Retired teachers can act as mentors, and online classes exist in wild variety.
2) Homeschoolers report that their child has more time and opportunity to socialise with people of all ages who can have meaningful connections to the child. If your daughter enjoys playing with her brother's friends this isn't unusual or a problem, she may have just found a group that is more suited to her tastes. Even some of the school peers may be for fun to play with when she isn't forced to deal with them all day "as a group." I think it's a quality time over quantity time question.
It could be that once the pressure of "holding it together for school" is off, your daughter may find she enjoys some of the group activities she now dislikes. Or she may still hate them, but may love homeschooling so much that she is willing to trade them for the privalige of homeschooling.
Of course homeschooling isn't the only way. A combination of gradeskips and subject accelerations can go a long way towards bringing your daughter closer to her academic readiness level, which may (or may not) give her a wider variety of kids to become friends with. Her being a "march to the beat of her own drummer" kid may actually be an advantage if she's going to be taking middle school classes this year and high school classes next year. If she isn't going to have a great time socially, she may as well be learning how to work hard at learning, IMHO.
I have friends who have made the pubilc school work their for 3 profoundly gifted children through gradeskips, subject acceleration, and college classes during the schoolday. ((Yes Mom drives 40 minutes each way, but the school got the ball rolling and cooperates in every way.)) They say that every relationship has areas of overlap where the two people can enjoy each other. I think this is a wonderful way to look at the world. It means that anyone can enjoy anyone, but perhaps can't share as widely with some as with others.
I do think that there is a big difference between judging a child and having the imagination to see how things could be better and giving a supportive push in that direction. It is as though you are hearing the tiny unhearable parts of your daughter's personality, asking for a hand.
I would also reccomend the book "High IQ kids" from Freespirit Publishing. It has a terrific article about multiple gradeskips and parenting kids who are as far "out there" as your daughter.
Great fun talking with you,
Trinity
