I heard about these very often.
Most of them choose 1 international kindergarten/class and then 1 local kindrgarten. But I also heard some choose 2 international kindergatens for the kids.
Usually these kids just have lunch and take a short nap in car and then go to school again.
It all depends on your child's sleeping pattern. If your kid sleeps more at night and doesn't take nap (or very short) in the afternoon, then that's should be okay.
Those families I know usually send a maid and a driver to take care of the kid during the lunch period. Then the child can eat and sleep/take a rest in car before PM class.