I have been pulling all sorts of trailers for over thirty-five years and have yet to encounter a tire imbalance causing what you are describing.
Not saying it wouldn't but I'd look at the tire/axle assembly alignment as measured from the trailer tongue.
Simply take a decent tape measure and from the front of the ball recess measure to the same point on each axle - I use just inside of the hanger assembly. Do not measure to the front of each tire as this will cause a spurious measurement - you have to measure to the closest fixed point on the axle assembly.
I've had brand new trailers out of square over 1" which caused the tires to vibrate as they wanted to go in a different direction than I was pulling. The out of alignment caused the tires to "climb" and hop which set up all sorts of weird vibration being felt in the truck - and not to mention beating the snot out of the tires.
I have also had loose bearings cause what you describe. To check just grab each tire at the 10 and 2 position and push/pull horizontally. Watch for the rim to wiggle and listen for a clunking noise.
Both of these are a especially severe problem when you buy a new trailer and it has used tires and rims instead of a new, matched set.
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