2002 Ford Taurus shimmy

My high mileage but very reliable 02 taurus shimmys like a wheel is out of balance when accelerating. This is even more pronounced when under load like when going up hill. Coasting, accerlerating downhill and running on flat surfaces the car is fine. The tires are fairly new and well balanced. Also, the transmission was totally rebuilt at 190,000 miles including a new valve body but I had it back three times before they got it right. Two of those times the car had to be towed. Does that mean the transmission was removed from the car three times? If yes could my problem be CV joints or axels or both. Also, the top motor mount looks to me like the rubber might be cracked or seperated and the problem did exist even before the transmission work was done only not as pronounced.