If it is just a feeling it is normal axle wrap. It is a normal issue on all 2nd gen Tacomas. Turning on your AC really gets it to move around at a stop.
It really isn't a big deal. It's a slight bump when at a light but it fells like someone hit you. Just keep your foot on the brake and pay attention to your rear view.
It's normal. These transmissions have tight converters and weak leaf springs. Should it happen? No but no vehicle is perfect. The rear of my buddy's GTO moves up and down as you shift from reverse to drive because of the torque from the engine. That doesn't mean there is something wrong. Chrysler FWD transmissions make a rattle sound when shifting back to first. Nothing wrong there either.