Unfortunately, Wizards hasn't released any season of Encounters for use outside of the program, most likely as an incentive for players to participate at their FLGS and a reward for those who DM.
However, there are still some other options. If your children are a bit younger, I would recommend trying
The Heroes of Hesiod. If they're older, then obviously you can start with something like
Keep on the Shadowfell,
Khyber's Harvest,
Bloodsand Arena or the Kobold Hall adventure from the back of the Dungeon Master's Guide, which you can get in a nice, properly-scaled
map thanks to NewbieDM. Or, if you have particularly imaginative/creative/zany kids (think
Axe Cop), then perhaps Gamma World might be a good fit for you. And if you've purchased some of the Essentials products (Red Box and Dungeon Master's Kit), there's an adventure line presented in the introduction to
this article, although some are solo adventures and will need some adjustment for multiple players.
There are also
plenty of pre-gens floating around in case you'd like to save character creation for a later point in time.
(Please note that Season 3 characters have some errors/omissions and Red Box characters will need to be
converted for continued play)
