RE can't losen the lug nuts..
You are right that they should hand tighten - or actually better - they SHOULD tighten with a torque wrench - which tightens them to exactly the right level per the Mfgs recommendations (My local shop actually has attachments for their air wrenches to do this - and the tire jockey is handed the right one for your car, and must hand it back at the end of the job - so he always uses the right one!)

That said - get yourself a "4 way" lug wrench - MOST people, including fairly lightly build women can loosen lug nuts with one. Also carry a can of "penetrating oil" (My favorite is Kroil) and spray the lug nuts oh, 5-10 minutes before you try - pop the hub cap, spray the lug nuts, put the jack under the car, jack until the jack JUST starts to take a bit of weight (just enough to prevent the jack from moving - 99% of car weight still on tires) - NOW try breaking the lug nuts - just 1/4 turn or so.. NOW jack the car, and then finish removing the nuts