2011 Silverado braking vibrates during downhill

Sounds like you're overworking the truck brakes. Check the adjustment of the brakes on your trailer. Trailer brakes need to be adjusted often as they are not self adjusting. Dexter says every 3,000 miles, as I recall.

Do you manually downshift your transmission? Most all hills I go down are done in 4th gear and sometimes 3rd if it's really steep. It helps keep the speed down. I also have the exhaust brake which works well.

Also, could you be towing too much trailer or not have enough truck?