A tad late to the discussion, but anyway...
I don't have kids, but I'm a tad introverted. I'm the son of the most introverted person I know, so I guess I'm in a sort of mirror image of your position and your kids
@yorkshirecomrade . I get on fine in social situations but I find it exhausting.
When I was a teenager, I remember when my dad was not letting my brother go to some party. My brother was really annoyed and accused my dad of stunting us socially, by denying us these experiences, and of making us lonely like himself. That of course wasn't true; my dad only wanted the best for us. But he took it to heart and it is the only time I've seen him, usually stone faced, visibly hurt.
I've remembered his answer, and think about it often, for about ten years. He said that if you
choose to be kind, generous, good humoured, honest, brave and if you don't take yourself too seriously, then you can make up for any lack of social skill. The people who matter won't care that you're not the most slick or charming person. Would you rather be a John Wayne or a Hugh Grant?
It's working for me. I have about 5 friends - not including my dog. It doesn't bother me that I don't have more. These are real "bury a body buddies." Interestingly, they are all massive extroverts and socialites. As a group, we have some balance, their extroverted qualities push me to go out of my comfort zone, and my more introverted qualities, I hope, encourage them to be more considered and thoughtful.
I'm not saying social skills don't matter and I agree with the above advice: practise social interaction but recognise the values of introversion, read
Quiet. Spending time alone is no bad thing, necessarily.
Also, don't fret. You have a family; you must be doing something right.
Sorry for the rambling, I hope there is something of value in the above.
From a fellow Yorkshireman