Car changes lanes on its own

So do you now have mis-matched (not identical) tires on the front?

Red flag, Caddyman caught it first. You have to replace the front tires in pairs, unless this is a 4wd, then all 4 have to be replaced.

Another red flag to me anyway is the cross rotation. I have seen too many times when this causes a belt in the tire to delaminate. That can also cause your problems.

So far we’re dealilng with four basic categories of possible causes;

  1. a bad rack (specifically the spool valve bleeding into one side of the rack when it should be in neutral)
  2. a serious alignment problem
  3. mismatched tires
  4. a dragging brake (including a parking brake)

With the added knowledge about the steering wheel sometomes shaking and the brake work having been done, I’m inclined to suspect a dragging caliper.

However, the OP knowing nothing about cars, I think a good shop is in order and should be able to diagnose the problem definitively. I’m puzzled as to why a problem this dramatic cannot be diagnosed.