Regardless of the cause, your front brake pads have become overheated and must be replaced for safety reasons. They may break apart unexpectedly. The shaking steering wheel indicates that excessive heat has damaged the front brake rotors which should also be replaced now.
Assuming this overheating does not happen without the trailer:
You may be towing too heavy of a trailer or driving too fast or braking too aggressively
while towing. Use of a trailer brake (a brake system on the trailer itself) may help. If you have a trailer brake it may not be working properly. You might also have a trailer that is loaded too heavily towards the front reducing tongue weight. Consider shifting weight on/in the trailer rearward.
If only one of the front brakes hets hot and stinky, you probably have a restricted brake hose or a hanging brake caliper which should be replaced. You could also have a problem of rear brakes working poorly. If the rear brakes are drum type, check for correct adjustment and normal operation of the automatic adjusting mechanism.
Your front brake rotors need to be machined or replaced.
You need the front rotors machined or replaced.
YOUR FRONT ROTORS ARE WARPED. YOU NEED A BRAKE JOB.
This is usually a symptom of excessive run-out (warped) on front brake rotor or rotors.
2 possible issues, warped brake disc, or failing steering dampner.
It is likely a brake rotor has to much run out (warped). There could also be some problem with steering or suspension components.
Only if your towing the vehicle by the rear wheels. If you are towing by the front wheels you do not need to unlock the steering wheel.
You probably have severely warped front brake rotors. Machining or replacement of the rotors would be necessary to correct the problem
worn front end parts (steering or suspension) could cause a car to shake when appling the brakes.
front brake pulsation have front rotors replaced
There could be a bad wheel bearing or worn front end components. Check the tie rod ends and ball joints for wear.
usually steering shakes over 60 mph is due to front tires needing to be balanced unless you have something more serious going on.