Get the fronts replaced also and odds are you will no longer have problems. Provided the suspension and steering is in good shape. The tires were old and you don't know if they had been abused by hitting or driving over curbs or other debris. The fact you had a shimmy probably means you had a belt broken or separating. New tires all around and have a competent mechanic check out the suspension, steering, drive train and brakes before towing again. It is not only your life on the line when towing with marginal equipment. All of our families are out there on the road with you.