All -- your help would be greatly appreciated. I bought my parents a 2000 LeSabre Limited a couple of years ago, and it has been a great car. It was purchased from the estate of a 30 year Buick salesman and was in immaculate condition with complete service records. It currently has 76000 miles on it and has developed what is best described as a side-to-side shimmy/shake/vibration when accelerating between 45 mph and 55 mph. It only happens while your foot is on the accelerator between those speeds and there is no noise associated with the vibration.
I had the tires taken off and there are no bent wheels. No alignment/balance issues. Tires are Michelins with 16000 miles on them, and rotating them made no change. I also swapped all four wheels/tires with those off of my Dad's Impala and no change. I've had a Buick master mechanic replace the front tie rods, axles and motor mounts and no change (it needed the motor mounts though). Transmission shifts smoothly up and down with no hesitation or roughness, fluid is cherry red and filter was changed at 60000 miles. Car consistently gets 25 mpg in city, 32 on the highway. Master mechanic says the only thing left is the transmission and/or torque converter clutch, but he's hesitant to recommend spending the money to open/rebuild the transmission in fear that it may not be the issue, especially in light of the low mileage -- he's been honest and said he's stumped and would have 'bet the farm' on the problem being a either bent wheel/bad tire/tie rod/motor mount/axle. No service lights, and no codes set. Mechanic also is seeing no codes in operation.
Has anyone else experienced this issue, and have any feedback or suggestions we might have missed?