Quoting BBBBB:" I see what you're saying with not using the word no so much and that's a good idea. I understand she ... [snip!] ... she couldn't accept it so I turned around and took her home. What could I have done differently in the situation do you think?"
You did right by taking her home, that showed her that if she acts out then she doesn't get to be rewarded. I would not have done anything different in that situation. Three year old's are starting to assert their independence so give her chores she can do on her own and activities that she can lead. Like picking up her room, letting her choose what is for dinner( you give two or three options and she picks which one). Play a game like "Simon Says" or "Follow the Leader" with her and take turns being in charge so she can see that it is OK for other people to lead and teach how to take turns. When you are out and she wants something and starts acting up because she isn't getting her way, give her a choice" if you behave then we can continue ______. If you continue acting mean (how ever she is acting) then we will go home". She will learn that when she behaves she gets to stay out and have fun, while if she misbehaves then she goes home and has no fun. Most toddlers/preschool age do better when they have options and get to feel like they are making the important choice in the situation than if they are told how to act.