teaching kids on the road or distance learning

He could start here.

http://www.aussieeducator.org.au/education/specificareas/homeschooling.html

Di

I'm a teacher.
I wouldn't just assume that I could pick up some books and "keep it going from where they were up to". I know that I have many parents who are totally confused re the "new" method of subtraction that came in 20 years ago, and it may even be necessary to slip in a very useful parent/teacher meeting to fill you in re their progress so far and how to keep it going.
Get your brother to contact their teachers or principals. It's been a few years since I had a student do "the lap" and I know that my boss would know more of the finer details.
I'm assuming the 13 year old is high school and therefore things will be different between the 2 school age kids.
The teachers and principals should be enthusiastic about the life lessons that the kids will encounter and will be able to guide in the right direction.
:)

Some families manage on the road education very well but there are also many who achieve very little and just vaguely talk about "how much the kids learn as we go". A high school age child especially will bel very disadvantaged when he returns if he has not kept up with the basics. A lot of the 'home schooling" material around is American based and not always suitable. Home schooling requires a lot of time and effort from the parents. Kids don't just pick up basic stuff by osmosis. Time has to be set aside for some proper effort. However, if parents are willing to put the effort in to structure some teaching and learning time it can work well.
As an ex teacher I had students whose travels involved sitting in a vehicle for hours at a time and seldom even being taken to local museums or places that could be interesting or educational to them. I had others who thrived, learnt a lot and came back up to standard in basic maths etc and able to return happily to school.
The parents we have met teaching kids on the road successfully all set regular time aside for some formal lessons. It does not have to be as much time as a school day as with only one or two kids you can get along quite quickly and there aren't all the other interruptions of a school day! The most successful seem to be those who join their state's Distance Education School so prepared lessons are sent out and parents don't have to do all the preparation. The current school will be able to give the appropriate information about this. Also kids can write emails and letters to their grandparents and classmates and keep a trip diary/scrap book. Their current schools will usually help set up something. This is a good way to maintain their English skills and keep in touch with friends. The diaries become treasures for the future.
Remember while Dad is having his 'trip of a lifetime' the kids must also enjoy the experience and not be disadvantaged when they return to school. It can be done - with serious effort. Lynne

https://www.youtube.com/watch?v=zDZFcDGpL4U