Part-time homeschooling is allowed in some areas, not in others. (Mine, sadly, is a "not.") Each school system gets to decide for themselves, I believe. But at least a couple of people on the forum are part-time homeschooling. 'Neato? Are you around?
Some people homeschool year-round, and so can take a week or month off in the winter if they don't feel like working then. Others take the summer off. As long as you get your hours in and keep the kids up on the work--not hard to do with a GT kid!--it's really up to you what you do in the summer. I try to get one official learning thing in per day in the summer, but as long as the kids are outside playing, I don't worry too much about it. That stuff matters, too!
Socializing is a lot easier for homeschoolers than most people think it is. There are groups for homeschoolers in most areas, since we all want to get out and play. Some people form co-ops, parent-run groups that combine group learning opportunities and play. I mentioned the "school for homeschoolers" that we discovered in our area, which is like a co-op, but has paid teachers and set recess times. And then there are more generic social opportunities like Cub Scouts, swim class at the YMCA, sports teams, art and music and language (etc.) classes, LEGO League, GT enrichment classes, and play at the local park or with the neighborhood kids.
Really, it's not AT ALL hard to find social opportunities! That's so easy! I really don't understand why people always think that's a big deal. But it's the #1 question that people ask.
For me, the hard part is having to be social every time my kids are. That can get difficult for an introvert. You find ways to cope...sitters, trading child care, co-ops and classes that allow you to drop the kids off, etc. It gets easier as they get older.
If I can answer questions, I'm happy to do it. Never any pressure.

I just want people to understand the truth and not believe the myths.