I think some public schools have an Independant study option that you could use. If you're going to return to your current school talk to your principal and see if they can provide the work for the year. Maybe.
There's also virtual k-12 public school, free to many districts. Your kid can do their school online anywhere with an Internet connection. Maybe that would free you up to travel. You would just have to ensure that it got done. You wouldn't have to teach or come up with lessons. I don't know if that's still available if you travel overseas.
