Some tread designs track the grooves and other road characteristics than others. Wide tires do that. I would think that a good alignment shop should have the capability to minimize that.
Does the car behave that way with both sets of tires? I learned, years ago, that larger wheels/tires specify differing alignment specs. Different offsets will also have effects. Hopefully, this is not a case of the C-beam missing, as one horror story read. I would, however, ensure all those bolts are tight.
Your alignment shop should also (if you cannot) check for worn or loose components which should have been replaced before ANY adjustments. Things are moving during suspension travel that shouldn't be moving.
"Dartiness", redefined as responsive handling, is considered a plus in racing!
(not on road dips).