The phrase "swaying trailer" refers to a situation where a trailer (attached to a vehicle) moves from side to side in an unsteady or unstable manner. Full definition
Stabilitrak with Trailer Sway Control automatically detects a swaying trailer and applies both the vehicle and trailer brakes to help bring it back in line. (phillipschevy.com)
Stay steady with StabiliTrak which automatically detects a swaying trailer and applies both the vehicle and trailer brakes to... (smartcarguide.com)
Stay steady with StabiliTrak which automatically detects a swaying trailer and applies both the vehicle and trailer brakes to help bring it back in line., TEXAS EDITION for Crew Cab and Double Cab models. (commercialtrucktrader.com)