When going uphill and the transmission starts to downshift the car starts bouncing like its on a washboard road. If I press the accelerator it smooths out. and if I can tell when it's going to shift and press the gas it is OK. I have replaced the fuel pump and all filters so I no it's not a gas problem. The accelerator cable seems to be slack to me but the only time it does this in on a hill.
I guess I was not to clear about the vibrating problem. I am sure it is not a fuel problem as I have just replaced the fuel pump and the filter and it does not matter what the fuel level is. When going uphill it is running smooth until it starts to shift into a lower gear, (it is an automatic transmission) then it starts to feel like it is on a VERY rough road and/or the tires are REALLY out of balance . If I press the gas it smooths out. If I can guess when it is going to change gears and time it right I can keep it from happening. By pressing and releasing the gas pedal when I think it is going to happen it does not happen and by doing this I can very often make it all the way up without the problem,.
Hope this will let you better understand my problem.