I just guessing here without seeing your vehicle..
If it were me, first thing I would do if it only does it if I am towing, have Trailer Tires and Rims Balanced (Some shops don't even believe in trailer tire balancing or use a bubble balancer) check for proper air pressure, out of round, separation, bent and balancing, bent axles, shackles and bushings and suspension bolts. I always get my
tires Road Force Balanced (Type of balancing can play a big issue). I would also make sure you have proper balancing of weight on each axle of trailer and tow vehicle including Hitch Coupler. Get a before and after axle weight with and without your trailer hooked up then do a comparison and make sure you don't have the coupler under or overloaded..
Next, if problem still persists, I would have the tires and rims checked on the tow vehicle including for out of round or bent, Than have them
Road Forced Balanced.
Next, If problem still persists, I would get suspension linkage, tie rod ends, bars etc, checked and get alignment checked. I saw a thread posted here I believe about front end alignment could cause Death Wobble and how to fix it.
I also use
Centramatic Balancers if I have balancing issues on all or any of my OEM Wheels if there is a problem with the OEM Wheels and leave them in place whenever I replace the original tires/wheels. These unit are a little pricey.
I would start with Tires and Rim first as they are the most common Issues in my opinion unless you are running Larger Size Wheels/Tires or Spacers.. Some of these things you might be able to do yourself with out having to go to a tire or front end shop.
I hope my ideas can help you out as sometimes these things are sometimes hard to trace down.