We’ve been homeschooling our daughter now for almost two years.
She routinely gets together with her old friends from school every week or so. In fact, they are in some of the same extracurricular activities.
She interacts with a whole bunch of kids several times a week at our gym, where she takes badminton classes. The kids are all ages, ranging from preschool into their twenties.
She interacts with other kids who share her online classes (Skype). They also email and Skype each other outside class.
She routinely texts, emails, Skypes, etc. with her friends.
Most of her interactions are online, with others who share her interests, which include digital graphics, animation, fan fiction, and gaming (League of Legends is the current favorite).
Her academics are a mix of tutoring and online classes.
She is currently eleven. I don’t think she is isolated, and she is very much in control of her friendships and relationships.