I frequently drive my friend’s Rav-4, which has electrically-assisted power steering, and I have nothing but good things to say about it. So, the OP’s assumption that the problem is electrically-assisted power steering per se, is not valid, IMHO.
However, there could be a problem with the way that Hyundai has set up the electric power steering on all Tucsons, or there could be a specific problem/bug in the OP’s individual Tucson.
My suggestion is as follows:
Take a test drive in another Tucson of the same model, and with the same engine, in order to see if it steers the same way that yours does at highway speeds. If the test vehicle steers differently (better) than the OP’s, then the OP needs to again tell the service manager at his dealership that he wants this problem resolved. If they refuse, or are unable to resolve the problem, then the OP needs to “kick it up a notch” by initiating a complaint with Hyundai at the corporate level. Contact info can be found in your Owner’s Manual.
If the test vehicle steers the same way, then perhaps this is a design defect in Tucsons. In that case, the OP should file a complaint with NHTSA, via their website. If there are enough complaints of the same nature, then it is possible for NHTSA to force a recall of these vehicles.
The OP should also begin to educate himself/herself about the Lemon Law in his/her particular state. In most cases, they get three attempts to repair a serious problem before the protection of these statutes can be applied, but this does vary somewhat from state to state. In my state, a successful Lemon Law claim gives the buyer the choice between a full refund or a replacement vehicle. In other states, only a replacement vehicle is possible.
Educate yourself!