B.M.
I taught my daughter that there were things she could make decisions about (I called it "regan way") and there were things she just HAD to do (I called it "mommy way"). the mommy way was NO ARGUING - ie car seat, brush teeth, hold hands in public etc. Around 3 years old was when she started wanting to do it ALL her way, so differentiation was very helpful to her. I started giving her freedom on things she could "choose" ie: pick a pair of pants, which veg do you want for snack and really emphasized the stuff that she got to make the decision. Then when it was a "mommy way" there was NO alternative. And if she didn't want to do it all activity stopped. Don't want to hold my hand? We don't cross the street. Can't cross the street - no park today. We HAVE to cross the street for an appointment you must hold my hand, if you don't we will be late and there will be NO play time at home etc etc etc.
We only really had about a week of transition and she was so elated to have so many things she could pick that she short of eased up on the dictatorship of the rest of it.
Good luck - 3 was by far the toughest age..... but she's only 10 now, so teenage is coming!!!!!!