I've gamed with my kids, I think most importantly you have to look at RPG gaming as you would playing a board game or any other "traditional" gaming. #1 you should be having fun and using the time together to create future fun memories. How would you act if you play Monopoly, or Sorry, or Scrabble with your kids? Obviously you try to win and do it in a way that everyone has fun; there is no reason a game of D&D cannot follow the same precepts. Losing sucks no matter what age you are; fortunately, the open ended structure of roleplaying games allows most games to end with a "win". To this day I prefer these sorts of games over "winner take all" types of games because of the positive feelings everyone gets when they leave the gaming table.
My one suggestion would be for the parent/GM to adopt a less "hostile" or adversary relationship that can be the case in most GM/player relationships. Don't "let" them win, but definitely don't treat them as you would a gaming group with two decades of experience. Give the kids a chance to retreat in the face of superior foes or attempt to solve a puzzle more than once. Less death traps, more "capture" traps, etc. Because it is the parent that is presenting the challenges, a parent that relentlessly hammers his kids by TPKing them, making them slavishly obey rules, or berating them for not solving a problem correctly runs the risk of turning them off future gaming completely. This is not to say you shouldn't hold them responsible for their actions, but the variety of responses available in such a game means that their ingenuity will be rewarded more often than not if they approach a problem from a "non traditional" point of view.
From personal experience, making the game an enjoyable one will have great rewards. My own father had no concept of "taking it easy" on kids when playing any sort of game, doing his best to crush us into the ground no matter if the game was Monopoly, Rock em Sock em Robots, or Electronic football. The end result was that we stopped playing games with him completely at a certain point, and certainly never invited him to play with us by the time we were teenagers or even adults due to the bad taste it left in our mouth. Gaming now with my kids I realize all the enjoyable times he missed with his kids because of his behavior.