I will throw in my penni mbili. All your descriptions of the problem point to the transmission..
Basically,the most logical approach such a nagging problem is by the process of elimination starting with the simple things such as mountings before moving to the transmission. So lets start;
Engine and G-Box Mountings- Checked and OK
Automatic Transmission Fluid- Drain to check condition and any particles from worn out clutches. If it is dark red or brownish,the ATF needs to be replaced. If there are particles,this could be a sign of worn inetrnal parts. If it has a sump,remove it to check the filter and any particles. If all is OK,please proceed to the next step.
Torque Converter- As Wally5 has pointed out,this is the most probable cause. Please also check for blue/purple areas on the surface which signals overheating,a major cause for failure. If all is OK,please proceed to the next step.
Open the G-Box- PLEASE NOTE THAT THIS IS A LAST RESORT AND MUST BE DONE BY AN EXPERIENCED TRANSMISSION MECHANIC. Most automatic G-Box function on hydraulics using the valve body and in-built piston(s). If the piston(s) are worn,the car will vibrate on drive.
Best of luck.
reithi