I have a 2000 SSEI...My question is whether or not a REAR trans mount (firewall area) could cause a vibration in the steering and passenger seat or cabin while driving down the road? I have replaced the front trans mount near radiator as well as had all four new Uniroyal Tiger Paw Touring tires road force balanced.

Seems also to be a little bit of "sway" feeling from the engine area when accelerating or variating speeds of throttle.

Thanks for any help...
TTERZ

the control arm bushings, cradle mounts, upper strut mounts, and lower ball joints should be checked, a engine mount is not going to give you a sway feeling

With a trust worthy friend'* foot firmly on the brake, transmission in drive, pop the hood and have your friend rev the engine up and down a little. Not enough to move the car. Shift between reverse and drive a couple of times. See if the engine is jumping at all.

Like Justin said, problem is probably not a mount, but you can determine if the mounts are okay or not.

If the vibration more pronounced when turning?