Wow are you raising my child? lol! My oldest dd is an extreme introvert. I probably lean more toward extraversion, but I like quiet time to read and do other things that don't entail having the house filled with noise. Dd#2 is a huge extravert. She started talking at 5 months and never stopped. She really wears out everyone else in the house. Dh is also very introverted. I feel bad for her b/c I don't want her to feel rejected since the rest of us need more quiet than she can provide.
Honestly, I think that it is more important for me to homeschool her than it would be for my older dd. We did hs dd#1 briefly in elementary school, but she is doing well in middle school now. Being introverted seems to help her be more secure in her own skin & less interested in trimming herself to fit in with whatever is popular.
Dd#2 is turning into someone I don't recognize at school b/c she is so concerned with the social implications of being different (including being gifted). She is eager to distinguish herself from her very academically successful sister and the rest of the family b/c we are all a bit different from herself. She is, therefore, rejecting intellectual pursuits in favor of make-up, goofy jokes, and things that make her appear "normal." If we can make it work financially, I intend to have her fully home next year.
You just need to move to Colorado and we can put together a co-op
! That actually was part of what I was going to suggest -- do you have a hsing co-op anywhere around you? You probably cannot provide all of the social interaction that your dd needs so I'd see it as very important that you get her involved in a lot of activities with other homeschoolers.