You can do it! Hang tight.
Your children will not be socially inept. In fact, most kids that I know who have been homeschooled are able to go on to college before their peers (I know a young lady who got a full-ride to CMU last year), know how to deal with all sorts of people - not just their peer group, and tend to be a lot more polite. There are networks of homeschoolers that you should get in touch with. One of the mommies I know is always taking her kids on a homeschool field trip or event.
I can understand their position; however, in a classroom w/20-30-40 kids, they aren't expected to actually respond to every question because the focus isn't always directly on them. It might be quite intimidating to them because they can't hide like they did in a classroom.
I don't know your reasons for homeschooling, but you need to be clear with them about those. Also, remember they are in that adolescent angsty period where everything you do is going to be wrong and hormones are running wild.
Stick with it for awhile - for some families homeschooling works well, for others it's not the right arrangement. If it doesn't work out for you, don't consider it a failure. A lot of people don't have the guts to try. 8-)