I have the same problem with my 3 yr. old. I can't catch him when he runs so I had to decide what was more impoortant. I constantly hold his hand when ever we are out of the house, from the time we go out the front door to when his buckles are fastened, to getting out of the car until he's strapped into the shopping cart. Everywhere! I don't put myself in situations that risk his life anymore. He got out of McDonalds and ran out in traffic, one time he ran out in our street and a pickup barely missed him. So I know what it's like to have your heart stop from fear.
You have to decide right now how you are going to handle this. I don't take J anywhere without another person going with me. I leave him in the car with my husband at Wal-Mart very often. I don't have the issue with the shopping cart because he gets a swat on his hiney if he gets up. My husband and I go together to shop for groceries and things and that really helps.
Get a babysitter when you go to the store, you might share the job with another mom who needs a baysitter too, you can watch one day and she can watch the kids another day for you. Find a Mothers-Day-Out program and take the kids one day a week or more. You can do your errands those days. She will eventually grow out of this but her life is in your hands right now.
Take some Love and Logic classes, they will help you set limits with her and teach you how to make her consequences very useful. We found our class at a local Mental Health Facility. They also offered them at a local elementary school this year.
Let me tell you a story.
When K was 2 and 3 she would take her shoes off everytime we got in the van, so every time we got out I had to crawl in the back and hunt for thrown shoes, even had to start carrying an extra pair in case I couldn't find both of the ones she took off. I felt angry at the wasted time, had to plan extra time to hunt for shoes, and was getting tired of not being able to find them until I took everything out of the van to get access to under the seats. So while taking Love and Logic classes I started thinking. I was always telling her that her feet would get cold if she didn't keep her shoes on. But she never had consequences from it so how was she supposed to learn. I made up my mind. I was going to try out this stuff I was learning even if it made me feel like a horrible mom. The next time she took off her shoes it just happened to be snowy and icey outside. I plopped her down barefoot in the driveway and shut the van door and started walking. She stood there looking up at me like I was the most horrible person in the world. I reminded her that she needed to wear her shoes outside and I was so sorry she chose to take them off. I walked to the house with her screaming at me to carry her. I didn't. She made it in the house, didn't die from being cold for a few moments, and has never taken her shoes off in the car again.
She isn't going to stop when you yell at her, she isn't going to suddenly start listening to you. She is probably going to regress some with the new baby because that's just what kids do. Me advice to is to make other arrangements when you need to go somewhere and take the stress off yourself until because until she's older you can't take thi risk.