These were exactly the concerns that I had. Connections Academy answered almost all of them. Yes, I'm pimping INCA out really hard. I believe in it a lot.
In INCA the parent isn't responsible for teaching the student. The student has a class and a teacher who sets the curriculum and course work. At the kindergarten level, there was more for my wife to do, because a 5-yr-old needs more direct guidance, but as the student gets older, they take more and more responsibility for doing the work. The classes are a relationship between the teacher and the student, just like in any school, and the parent's role is mostly supervisory. And, you have the benefit of smaller class sizes, so the teachers have the time to work more directly with each student.
There is less interaction with other children, no way around it. But, as you said, we have got our daughter in Daisy Scouts, swim lessons in the summer, and we spend as much time as possible with our family so she's around her cousins quite a bit. We also have memberships at the Indy Zoo and Children's Museum, and because the school schedule is totally flexible, we can go quite often - and that time counts as class time, too.
We may send the girl to a high school when we get there - it will depend on a lot of things. What I am certain of is that right now, she's getting the best possible education that we have access to.
I dug up the curriculum page that shows courses available at all levels:
http://www.connectionsacademy.com/indiana-online-school/curriculum/home.aspx