Conduct a safety drill, have your passenger yell out SWAY!!

Why on earth would you want to apply brakes to trailer tires that are already beyond their friction limit? That simply reduces the lateral restoring force available causing the trailer to swing wider, more likely to hit an oncoming car or a guardrail, tree or boulder.

The best you can do is keep both hands on the wheel, eyes on the road, and try to keep your vehicle pointed down the road, and hope for the best. Apply brakes after the trailer is realigned.