Regarding kids and non-dominant hand, try presenting it as a game. Use coloring or solving a maze, then drawing and maybe writing.
If the kid is old enough (I'd say from 7 y/old and on), make it a challenge, doing the same exercise day after day, for say a week, then compare the earliest and the oldest 'work', it's likely to be really improved. The brain, at that age even more, is really flexible and will pick it up in no time. 10 min a day and you'll see improvement (I used to do this when I was bored in class, writting the same line or doodling, or even just trying to take notes) but you do loose it quickly if you don't practice.
It's a good exercise because it forces the brain to adapt and use/create new neurological pathways.