Well, from my experience, I'm no mechanic, but I have the same sort of problem but my tracking/wheel alignment is all permanantly damaged. I bought the ti at a good deal but the kid thought the transmission and drive train was damaged. The issue is front and rear suspension. I took it to two separate blind tests for wheel alignment and both times failed with about the same specs as to what happened.
You see, kids buy these cars to mess with them and do power slides, burn outs, you know, all that douchy stuff, thus the ti was abused in such a manner.
So, I hope you don't have the same problem because its pricey. I have to replace front and rear suspension, it drives good though, a little rattle here and there, and my steering does the same as yours. These cars are built tough I will say, but I have to fix this issue as my rear tires are worn out very quickly.
Which incidentally, was an obvious problem that the suspension was all destroyed from a slide into a curb or something similar. | 
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