I agree with herroyalnotness - I'd written quite a long response and my computer crashed - damn - let's try again!
I think there is a distinction to be made between a holiday and a visit to family, perhaps, too.
I am a foreigner, married to a UK citzen, so we have a similar situation. I live here because my DH is here, and his kids are in school here and he doesn't want to move them (fair enough). In our case, I have a one-year-old DD and two teenage stepkids. The kids live with us fulltime, there is no other parent to consider or to look after the kids. When I met DH I was already in the habit of returning 'home' at least once a year, and he well understands that is not going to change! So then the question becomes 'who goes?' on those trips.
I've been to see my family (all abroad, we are extremely close, includig my parents who are elderly and unwell) twice since DD was born. On one of those trips, only DD and I went. On the other, DH, DD and I went a week earlier and the kids joined us a week later and came back with us after a second week with my family. The kids were in school, so joined us when their holidays began. They stayed that week with a friend, which they loved.
DH and the DCs have also been on trips without me and DD, to visit DH's family. Good! They will go on one such trip on their next school holiday.
In November, DH and I are planning a trip to Prague. It is a great work trip for me, and I don't want to miss out on it because 1) the older kids are in school, and 2) we can't afford to take the entire family. But I need/want to take DD because of her age, and DH is coming to watch her whilst I attend the conference. The kids will stay with the family friend again.
The reality is that I will continue to take DD home to see her foreign family every year. Sometimes all five of us might be able to make a holiday of it, but the expense is enormous, and frankly, I know that the kids wold prefer their annual holiday NOT be taken up with visiting my family (although they like them very much) in my rather dull hometown.
If we were taking DD on a pure holiday, to some place with no work or family connection, just a fun vacation, that would be different. I'd never expect, though, and neither does DH, that I would be kept from seeing my own family because of the kids' school schedules (unlike me, DH will not consider taking the kids out of school at all) or our financial realities.
I think there is probably not one automatic answer to this one.