1991 Chrysler front end shaking -- update?

My friend’s 91 Chrysler 5th Avenue developed a vibration and fairly strong shake at highway speeds during a heavy rainstorm. The shaking seemed to be in the front end and was affected by braking. It occurred mainly at speeds from 45 to 55 mph. The shaking was not so noticeable at in-town driving speeds. Several weeks later the car, after not having been driven for a few weeks and the weather once again wet, would not back up – it would shift into reverse but appeared to be hindered by something holding the wheels. The feel was much like an emergency brake being on. Finally, the car backed up and made a noise as if something was being run over. Since then the car has moved fine. Today, I took the car to a mechanic, and he found nothing wrong with the front end, front brakes, or tie rods. He did find both the rear brake cylinders leaking badly. He cleaned the area, replaced the brake cylinders, and drove the car with no problems. Question: Would the rear cylinders cause the shaking/vibration and the sticking/hesitation to reverse? Thanks

Yes the leaking rear cylinders could have caused the shaking. At the same time the cylinders start to leak, the cast iron cylinders rust and lock the pistons in place. So you may have had a dragging brake shoe or shoes. When the brake fluid leaks onto the friction material it can rust to the drum surface if the parking brake is left applied. This cwould be why you had the locked brakes in reverse. I hope the mechanic replaced the shoes and checked the drums for warpage if they also were not replaced.