Hang in there and start over. Many children just want to have control and they like knowing what to expect. I like to say they need to feel, like they have control, when in reality you are going to allow them control.
Give her a calendar and have her help decide how things are going to happen. "On Monday, what are you going to wear? Blue shorts or red shorts? White top or Yellow top?" Have her gather them the night before and have them ready. Have listed the activities, that need to get done. 2 loads of laundry, grocery shopping, then give her a choice, what would she like to do? go swimming or go to the library?
Same with meals, I always allowed my daughter to eat what we were eating, or she could have a bowl of non sugar cereal or peanut butter sandwich no big deal.
If we were going somewhere, I would let her know what was going to happen there and what behavior was expected, inside voices, no running inside and look with our eyes not with our hands. I always had her take a book, colors, paper, radio, something to keep her occupied. Many times, I would have her help me grocery shop. I would remind her, we were only purchasing what was on the list.
In the summer, I always kept a cooler with cold water, juice boxes, fruit and veggies in baggies.. We kept snacks in a bag also, this way, she always had a snack in case an event took longer than expected.. I also made her responsible for making sure that this was kept filled. She loved the responsibility.
She knew that if she threw a fit, we would leave.
EVERY TIME. Your daughter can be put in time out, even in public. Have her sit on the ground between your feet and remind her to calm herself down.
When we went to restaurants, if she knew she was becoming "frustrated" or needed to walk around, she was allowed to ask us if "we could go outside for a minute". We would even allow her to go outside and "scream" as loud as she wanted to release some frustration. It worked great.
We would give her 5 minute warnings, before an activity was going to end. "In 5 minutes, you need to begin putting away the toys." Then when it was about 4 minutes, we would say, "you have 1 more minute." It really helped. We used to laugh because she would ask for 5 more minutes or 1 more minute. Of course we would allow it if she asked politely. Or we would explain, "I like the way you asked for 5 more, but we just do not have time tonight."
Just stay firm and do not give in. She will respond to what the rules are, Especially if you have stated them.