I think you should accept that your children need to say "toilet" at school, as if is by far the most commonly recognised word and will be understood wherever they go, even by people who speak English in other countries.
I was brought up with "lavatory" or "lav," by parents who had been the first in their families to go to university and get "middle-class" jobs, and who were, I think, excessively worried about what other people would think about them so they always used the "proper" words. When I moved in with DH, who says "toilet," I couldn't bring myself to say "lavatory" in front of him because it sounded so pompous and hypercorrect to my own ears, so I soon adapted to say "toilet" and I taught my children the same word, because I knew it would be understood anywhere.
I would say "loo" is probably more widely understood than "lav(atory)" nowadays but I would still go with "toilet" as the universal, foolproof word.
I don't think many people worry about class any more, except maybe the very, very upper-class, and I'm assuming your children won't have to mix with them at school.