Which is the right move in a split second decision?

If the trailer starts swaying the option is to apply the trailer brakes. Then once it is back under control you slow down. Take your foot off the gas and keep the trailer brakes manually applied until you slow down.

You need to put tension on the joint between the hitch ball and the tongue. There are two ways to do this. Put on the trailer brakes while the vehicle is still under power. Or accelerate to attempt to fix a problem that is caused by going too fast.