I've played one session of D&D with my son and his friends. We got through 3 encounters.
I made the adventure up myself, designing it towards what I knew they'd be hooked into.
I also allowed the 3 kids to have SUPER stats. I got rid of Daily powers and each character has an awesome Encounter power somewhere around Daily Power strength. I gave each of them 3 At Will powers/stances and a Racial Power (including the Humans).
I flagged skills as such, skill rolls just based on Strength etc. and the Target DC being a standard 10 for anything they want to try. Each does have a Skill Power relevant to their class which they can use as an encounter power that lets them pull off something they imagine related to that skill.
It went really well, and they are all enthused to play again this weekend coming up. They are 5, 5 and 7 years old respectively.
As Zombies are the rage at school at the moment I made a zombie based adventure. Like you yourself suggested, I made the first encounter with a horde of minions. When they began they discovered their class mates sleeping at their desks were zombies. So was the teacher, the only non-minion in the encounter. So that was something like 16 minions and one normal zombie. The good thing about zombies is their low initiative. So That is 6 players (each parent playing a companion character with their child) having a go at them before they can react. Nearly all of them have some kind of Blast, Burst or multi attack power so by the time the zombies got to go there were 2 miions left and the teacher. But there were 3 windows through which another 9 zombies burst through, overturning the class science experiments. One of the tables set a large area of the class on fire and the other set off a magical immobilising web, leaving only a narrow corridor of free movement in the centre of the class. By the end of the next round all the minions were dead and they finished off the teacher as they let loose their encounter powers in the third round.
And then they had to deal with the class being on fire! The book glowing on the teacher's desk was read by the Mage using her Arcana power. It was marvellous to see her stand up at the table and wave her arms about with an abracadabra, which of course was more than enough to trigger the safety spell on that page, putting out all the magical effects in the area.
The leapt into the next encounter as they went into the corridor and heard some nasty growling behind the door to the vet's lab. They threw that door open no questions asked, itching for another fight. 3 zombie dogs (minions) and a zombie bear, a zombie gorilla and a zombie tiger which were reskinned higher level zombies from the monster builder. They were quite nasty and actually managed to drop the Paladin but they had the hang of their encounter powers by now and they mowed through them in 4 rounds. Focus fire was pretty natural here as they were stuck at the door way, only one of the big zombie animals could reach them at a time.
The third was kind of a skill challenge as they tried to reach the school 'Safe Tower' following the instructions left on the blackboard by their teacher. they had to go through the gym which meant going over an obstacle course. However a tower of Anti-Magic meant no magic could be used inside the gym. 4 Guardian Golems protected anyone trying to scale the tower in order to hit the button that would turn off the anti-magical effect. They also protected the equipment room where each had a magical object kept under lock and key that they would be given when the passed their final exam and graduated from Adventurer's School.
They could take on the obstacle course with their skills or face the golems and attempt to turn off they tower. The magical objects were the deciding factor and they took on the golems. They resolved the no magic inside the gym by using magic from outside the gym. The Druid turned into a hawk and flew to the top of the tower and hit the button. Magic came back on. We were 3 rounds into the fight and the pizzas for dinner had arrived, so I had the Druid roll a Wisdom Check (perception). He succeeded and spotted a second button that hadn't existed until the pizzas arrived which when pressed turned off all of the golems. Once the magical Items were retrieved from the equipment room the Wizard teleported up to the entrance of the Safety tower, the Drangoling, Tinkerbell and the Hawk-form Druid flew up their, hauling Scooby Doo (the Thief) with them. The paladin leapt through the obstacle course with his exceptinal strength and reached the bell tower which when rang called a giant bat, upon whose back he flew up to the entrance as well.
Minions were great. A mix of minons and a few tougher creatures works really well. Also having ways to end combat with other actions is a really good mechanism as well. I guess 12 is another ballgame. With 5 year olds i think it has to be super-action all the time. There is no room for reality there. Maybe designing your own dramatic adventure and getting some friends on board (and mum as well?) will make for a more exciting experience. I'd suggest house ruling HP, either allowing a higher point buy so that PCs can have a high CON score (which will increase HSurges as well) or give them a background similar to how 'Born under a Bad Sign' works, whereby HPs aer based off the PCs highest stat score.
Expertise is probably the first Feat to take. Missing sucks.
Finding a stash of magical weapons, or being awarded it, further increasing chance to hit is probably a good element to work into the story as early on as possible.
Anyway, don't give up! D&D is an awesome game in its many forms. Play it as you want it to work, that makes it as fun for you and your son as possible. Good luck!