I think you need some visuals.
Rafting the Zambezi.
Note 1: All of the rafts have a single guide in the back with 2 oars (not paddles). Given your situation of the kids are supposed to look like they stole the raft I can see the "only 1 paddle" idea.
Note 2: All of the customers are told to get low and hang on (Guides usually yell "Get Down, Get Down!") just before the big hits on all the rapids. The customers only have paddles to give speed at the top before a rapid. A skilled guide who knew the river could use a single paddle to get the appropriate speed before hand (this is how the gear boat is run on the Lower Yough in Pennsylvania, granted smaller rafts) but he would be beat tired by the end of the trip.
(check out 1:07)
"High Side Right!" is what the guide called likely called right before 1:07 in the video. Note how all of the people try to get as high up on the right side of the raft (the side against the rock). The goal of this maneuver is to keep weight off of the water side (up stream side) of the raft. If the side of the raft away from the rock goes under the water, the water will continue pushing the raft until it flips upside down. By keeping weight on the rock side of the raft, the water just rushes underneath the raft (ideally). That video is a great view of what flips against rocks look like.
Flipping in a "hole"
This video has a whole lot of cases where the raft went into a "hole" and then flipped. The "hole" or hydraulic is the white frothy pit in the river. What happens is the river folds back on itself. A flip in these cases happens when the raft drops into the pit and then the fold of the water forces the raft to go upside down.
Youtube "Whitewater Rafting Carnage" to see a whole assortment of raft flips and "getting stuck in a hole"