Do you think its because your personal links where you do live are to the international community not the local one? Are your kids more rooted in the local community?
International communities are always somewhat transient, there is always coming and going, someone is always talking about "going home". It must be hard to feel settled in a community of that nature.
We've lived in DH's home country for 11 years. My bouts of homesickness were horrendous in the first 5 years. They've gone now though. All I miss is the English language (but that is a massive deal - operating in your native tongue you can truly be yourself, and studying and bureaucracy are so very much easier)...
2 of our kids were born here and one can't remember living in Britain. I take them back because it's part of their identity, but Britain is their heritage not their home. I cannot imagine my kids ever living in the UK to be honest. They have roots, which are something I always wanted but never really felt I had as my parents moved a lot. I'm afraid I do agree I would not uproot settled children without an unavoidable reason (i.e. if employment was no longer possible where we are, or if it were a country where visas might be revoked, or if one family member was truly unable to manage - special needs not catered to, medical treatment not adequate, or truly depressed with a reason to believe a move would change that).
Do you feel fairly sure you would be happy if you moved "home"? I think there can be a serious case of rise tinted glasses for some people, especially if friends and family have moved on/ scattered and there is no slot to fit back into...
If you waited 5 years would your children stay where you now live without you? Might that actually be better?
Though I suppose having roots (for you in the UK but not living there) might be a problem too!
Is moving towards the local community and away from the international community not an option for you because they are closed/ unwelcoming or because of language? I doubt it's possible to stop feeling the way you do while all your local friends and support network are potentially transient and likely to move at some point.