I've played a game of my own invention with my little sister.
Basiclay its warhammer skirmish, made easy. Most of the special rules are ignored.
Basicaly you play it as a chain of games. You start off with one hero character. Then you play a sort of role playing skirmish game agians some bad guys that are lurking about a game table hiding in terrain. You find some treasure. Then in the next game the tresure is used as points to get stuff, like some troops or upgrades. You keep doing this till the story winds down.
My sisters first "story" went like this. She was a brettonian mage. Killed some orcs. Finished first part. Got some archers to help her. She went on like that gaining points to spend. She became second level, got some knights, a magic weapon and some men at arms.
I think its good because:
i) its fun
ii) it teaches the warhammer game system (ie. phases, points, combat mechanics)
iii) gets them into painting and collecting figures
iv) eventualy they'll want to use bigger armies, but by that point they'll have learned the game basics from your little ones.
And in case I forgot anything:
Little kid: good guys
Old guy: Bad guys (orcs)
Because you've left out the special rules things are a little unbalanced, so you will need to go easy or hard depending on the cirumstance to keep the game fun.
Hope you can all under stand that, I'm not very good at making much sence today.