If the stoker is about the same size as the captain, I don't see any reason to not give the stoker the shifters and drag brake. I happen to be stoker and much larger than my captain (she's 5'6", I'm 6'2"), but I could easily see adequately if I were much shorter. I have controlled the shifting and drag brake on our tandems for 28 years.

That said, if the captain is having trouble I would think the most likely culprit is the stoker. You've really, really, really got to ride quietly and give in to be a good stoker and to allow the captain to get a good feel. Are your hands out wide on the bars, or are you keeping them in the center of your handlebars to decrease your leverage when you rock? Are you sure you're riding like you would on rollers (you do ride rollers, don't you?), or are you controlling the bike a bit with your weight and steering it against what he's trying to do?

Just so you don't think I'm picking on you, here's something that I often catch myself doing. My captain likes a lane position that is further right than I would choose. This is particularly troublesome on two lane roads with traffic coming both directions but not enough room for a safe pass by the overtaking vehicle. I always want to be far enough left that no moronic motorist would ever think of trying to pass before the oncoming traffic clears. My captain will be a foot or two further right than I like. Often, I resist her lane position by leaning just a bit left. All that does is cause us to ride along with the top tube displaced to the left of the bottom brackets. It's uncomfortable and must look silly and annoys my captain. It's also 100% my fault and bad behavior for a stoker. As soon as I stop fighting the bike gets plumb in a heartbeat.