I don't think that sounds too bad, actually. If you are very rich international nomads, why not have someone who can home-ed your children really well, and cover all kinds of fields?
The only bit that really makes me boggle is the bit where the tutor is supposed to arrange play dates wherever the family is in the world. I'm trying to imagine teaching the children robotics and Mandarin and Tai Chi while frantically thinking 'It's Tuesday! We're in Singapore/LA/Toronto! Must find some unknown children to come round!'
There's a nanny for a ME minor royal (I think) family on Mn sometimes, posting about whether she should continue in this incredibly well-paid job that leaves her zero time for any kind of life, let alone meet a partner and settle down, or quit.
Her situation sounds much odder, though, in that she's a nanny, rather than a tutor, but she's the Executive Head Nanny, with a team of comparatively badly-paid under-nannies beneath her, and her job is managing the other nannies and the children's timetable etc.