depends if the fun is happening in turns(ing) - which it sounds like.
the trailing arm thing happens w throttle on/ throttle off "noticeable" even whilst going in a straight line. punch throttle and car will leap to one side (to the right irrc), take foot off throttle because throttle-on scared the crap out of you and car will jump the other way. when they are bad, at highway speeds, will jump almost a full lane. lots of fun.
if in a turn, most likely due to the trunnion bushings. trunnion is the only thing keeping the rear of the car centered over the axle... there are 2 bushing sets that keep the car located properly over the axle... the bushings at the pin on the diff and the bushings on end of trunnion where joins body. if one (or worse, both) are shot, the rear end will self steer shockingly. will wander in straight line, make a turn and will be totally terrifying. most likely the ones at the ends of trunnion, against body are long gone.. in the dwg above, they are P/N 1365 48420 - the thin dount ones. w them gone, the car will slide side to side over the axle (or vice versa) steering away. very exhilarating.
based on the condition of the car as already described.. i bet all of the above need attention.