Someone else may have to diagnose your problem, though it sounds like there's looseness in your front or rear suspension systems. You didn't provide much of a clue about what the wierd noise was when turning sharply. Is it a clunk or a squeek or what?
Some '91na's after 100,000 miles or so develop sloppiness or wear in their rear axle carrier-to-outer tie rod end spherical bearings. Having that loose rear end condition allows the rear wheels to rotate slightly around their vertical axis, as if there was a small amount of rear end 'steering' that you couldn't control. It would provide symptoms similar to 'hunting' you experience. I suggest this because you didn't mention that your mechanic examined your car's rear end... for that's not where one would generally first look for such a problem. To rule out that possibility, jack up a rear wheel off the ground, grab it at the 9:00 and 3:00 o'clock positions, and while pushing with your right hand and pulling with your right, then alternating, see if you can feel any looseness around that imaginary vertical axis. Repeat it on the other side rear. If there's ANY freeplay there, and their shouldn't be, replace the corresponding axle carrier so as to get a new spherical bushing (that can't otherwise be ordered from Toyota). If there's any wear or looseness in those spherical bearings, (i.e. 1/8" or so perceived slop as measured at the rear wheel when twisting like that), there's little danger of losing control, but the sensation is discomforting. Some bad tire brands of all-season tires can also cause that sensation of hunting on certain road surfaces.
Some '91na's after 100,000 miles or so develop sloppiness or wear in their rear axle carrier-to-outer tie rod end spherical bearings. Having that loose rear end condition allows the rear wheels to rotate slightly around their vertical axis, as if there was a small amount of rear end 'steering' that you couldn't control. It would provide symptoms similar to 'hunting' you experience. I suggest this because you didn't mention that your mechanic examined your car's rear end... for that's not where one would generally first look for such a problem. To rule out that possibility, jack up a rear wheel off the ground, grab it at the 9:00 and 3:00 o'clock positions, and while pushing with your right hand and pulling with your right, then alternating, see if you can feel any looseness around that imaginary vertical axis. Repeat it on the other side rear. If there's ANY freeplay there, and their shouldn't be, replace the corresponding axle carrier so as to get a new spherical bushing (that can't otherwise be ordered from Toyota). If there's any wear or looseness in those spherical bearings, (i.e. 1/8" or so perceived slop as measured at the rear wheel when twisting like that), there's little danger of losing control, but the sensation is discomforting. Some bad tire brands of all-season tires can also cause that sensation of hunting on certain road surfaces.