The TCM has nothing to do with the Traction control.
The transmission has nothing to do with TC.
There are other things besides a dirty screen that can cause the VVT solenoids to malfunction.
It is possible that the VVT SENSORS have a problem, since P0013 indicates that the cam position is not where the computer thinks it should be.
Could be a bad connection at the brake control computer; which is what controls the TC.
The likelyhood of the ECM having a problem other than a bad pin on a connector is close to zero.
Dealership shops suck

The causes of the traction control light are:
A. the button has been pushed to turn it off
B. a engine performance code is either "current" or "pending". A "current" code will cause the CheckEngineLight, a "pending "code does not.
C. a "pending" or "current" code will cause hard shifting, this has nothing to do with the TC