I don't think the motor mounts are the reason why you have a tranny error code. With the torque convertor clutch stuck on, the torque convertor is not disengaging causing the bucking. There is a constant TCC apply. It means you probably have a defective TCC solenoid or TCC-PWM solenoid on the valve body. To correct the problem one of them needs to be replaced.
On the driver's side of the tranny (top) is the 20 way electrical connector. Disconnect it and then re-seat it.
In the interim, you have nothing to lose by putting in an additive such as Sea Foam or Lubegard. Under $10.00 cost. It may help unstick the stuck TCC valve. The stuff works wonders on minor valve body problems. Good luck!
Thrasher CAI, DHP v1.0 PCM, SLP Headers,
3.25 SC pulley, CAIT GMAF, 2.5 DP/Hi-Flow CAT,
u-bend delete, 160 TS, ZZP Stage 1 72mm TB,
TB spacer, MSD 8.5mm wires, Autolite 103,
Goodyear Gatorback Serp. & SC Belt,
Nitto NT555R Drag Radials
1/4 ET: 13.210 sec. @ 104.490 mph
0 - 60 ft: 1.945 sec.