"Home" for Different Family Members

I was just mentioning in my previous post how weird I now feel in relation to the US and the UK. I've been gone from the UK for so long that not everything is comfy and familiar these days. However, all my family members are still here (in the UK), as are my long time friends from school, university and work. No matter where you go you can't replace them, (even if you'd like to) and I make a big effort to reconnect with as many as possible on my annual visits.
When I get off the plane at Heathrow, even though it's often cold (very early morning) and wet (well, it is the UK after all),  I can almost feel my shoulders relaxing. Very difficult to explain; I just feel like I'm back where people understand me; I'm not "the British woman",  no one turns around when I open my mouth or attempts a feeble imitation of my accent.
What is quite odd for me though, is that this is not my children's "home". We've been coming here every year (and sometimes more) for twenty years now. Back before they had their own lives, I would bring the kids for 7 and 8 weeks, dragging them from pillar to post, having them sleep in strange beds, playing with children they'd never met before and eating stuff like beans on toast. They were little champs and have very fond memories of those summers. As they grew older however, they started to want to get back to their friends or just their normal surroundings; they're American after all, even though they proudly tell everyone and anyone that they are also British citizens.
I always say they are bi-lingual; actually, not only do they know the British words for all sorts of things, they can also do a mean Geordie accent! Were they to live here, I have no doubt they'd feel pretty comfortable fairly quickly, but I wonder if they would ever think of it as home.
Another aspect of expat life - having a different "home" from your kids.