How to carry a large backpack on a bike rack? My 3 kids ride their bikes to school and carry 20 pound back packs stuffed quite large. They won't fit in any pannier I can find.

I've considered hanging them off the side of the pannier with bungies to keep them from shifting, and perhaps a sheet of stiff plastic to keep them out of the spokes.

Side baskets are too large for them to fit their bike @ the bike rack @ school.
I've also considered a very narrow basket on top of the rack but puts the center of gravity high, makes it harder to swing their leg over the bike, etc.

Looking for better ideas.
I too had this problem and found a somewhat unique solution. I explored using a pannier, but since I carry a laptop daily, I was worried about what would happen if the bike slipped on the ice and crushed my laptop bag (something that actually happened to me as a teenager) 

Like you stated, baskets are too tall and cumbersome, so instead I found a 19 by 13 inch metal serving tray and mounted it with heavy duty rubber straps. It even matches the color of my bike panniers so I think it's a good solution. It's very freeing to be able to carry so much on my bike without the constant weight on my shoulders.

 

Since the laptop sits at the bottom of the backpack, I feel like the metal walls of the tray should absorb the shock of a slip or fall and protect it inside. So far I've received multiple compliments on this design. It's been over a year now on my bike and has held up well.