I'd run the starter set as-is. It is marketed for just this purpose, so it should have plenty of tips to help the DM and will likely include nudges for the DM to give the players.
I've been doing D&D encounters now, off and on, through the entire playtest. The purpose, IMO, of encounters is to create enthusiasm for the game such that people want to go run off and play more on their own (and buy stuff of course). To that end, you can't grow wrong by encouraging enthusiasm. The starter set is not a 2+ year campaign so if things get a little out-of-hand, so what? Say yes to anything the kids seem to be enthused about. Try not to set the difficulty "realistically" but rather set it that its achievable by the PCs. Kid wants his character to swing down from a rooftop on a rope he hastily secured to a chimney and on to a speeding carriage? Awesome! DC 10. When they fail the awesome thing, don't be tempted to make it disastrous, rather make it such that they can still do something meaningful the following round: "A 7 fails. You swing down, but don't quite make it onto the carriage. You are on the ground next to the carriage and it is still speeding down the road. Next round you get +10 speed bonus from the momentum of your swing" (they'll need that +10 speed if they are to catch up to the speeding carriage)
I try to tell myself to simply "allow epic moments" when dealing with younger kids rather than my personal, more gritty DMing style I do with the adult group.
Don't be afraid to tell them (leading) their motivation explicitly. "These are the orcs that drove your family from the area. The same tribe that burned your families farmhouse. Do you really want to retreat? They killed Old Yeller!"
They'll be pretty clear about what bums them out and what excites them. That age group has a hard time with the poker face, and it doesn't occur to most to play against their own feelings for the characters. If it bums them personally, it bums their character, even if in the narrative fiction it should be happy news for their character.