We have homeschooled all of our 6 children. The oldest 2 are partway through college (both National Honor Society), one about to enter college. Three of the boys play travel sports and excel at it.
Each of them have their own personality that would show up whether homeschooled or not. One is shy, one is extremely outgoing, etc. I have noticed this in friends families that are not homeschooled. If a kid is shy, having them in school will not automatically fix the problem. More likely, they may be shunned by groups of others. You need to work with the shy ones to help them feel more comfortable, whether they are in school or homeschooled.
We were fortunate to be able to do things that helped them see stuff in action instead of just in books. For example, attending local town board meetings to see how government works. Roadschooling would be a great situation, but most of us have local jobs that mean travelling only during vacations.
Successful homeschooling/roadschooling is not rocket science. It requires determination more than degrees. Studies have shown that the education level of the parents have little effect on the outcome. For higher-level(high school) science and math, there are many homeschool co-ops that provide the necessary classes if needed.
Good Luck and God Bless.
Steve