You could also look at going down the Roaring Fork - It's way more chill than the Arky or Colorado. Defiance Rafting out of Glenwood runs those and does a fantastic job.
It's a little further drive (you'll drive past the upper Colorado turnoff at Dotsero and through Glenwood Canyon) but I see those rafts everyday passing the house and they appear to have a lower age limit.
You can also hit up the hot springs before heading back. Terrible way to end a day on the river

In terms of driving from
Breck: Browns/Numbers: 1:10 minutes
Breck: Clear Creek: 55-1:10 minutes
Breck: Upper Colorado (State Bridge) 1:15 minutes
Breck: Lower Colorado/Shoshone 1:05 minutes
Breck: Colorado/Roaring Fork confluence (Glenwood): 1:30 minutes
Moral of the story: regardless of what direction you travel (S to Browns, W to the Colorado/RF, or E to CC) you're only adding at max 30 minutes there and back regardless of where you go so find the place that resonantes best that you think they kids would enjoy.