Have you tried the driving carts. I know they can be a germ fest, but if you use the wipes (we use half the contain wiping th whole thing down) then she gets to do something. 2 is all about them deciding what they want to do and when (or when to be confined. I have actually see the staff at the 35th HyVee personally cleaning those.
also, my son loves those little shopper ini training carts and he does pretty good at staying with me, not running. Also, if I prep him for what's going to happen in the store BEFROE we go in, he's much better. Maybe when you getting ready to go, you talk about where she's going to sit, and what's expected, she'll feel like she knows what to do.
However, nothing works better than stopping and leaving the store. yes, you may have to leave a half full basket in the aisle, but as soo as she says "NO" or is bad in the cart, leave. Go to the car and explain that that is bad manners (whatever) and that you'll just back without her. There isn't really anything we purchase that we couldn't wait another 12 hours for. Then go back W/O her so she understands. Then the next time, remind her of how you had to leave because of her behavior and that you'll leave again if she repeats it. We only had to do that 2x, and have never experienced anything than idle chatter.
Also, be sure not to go when she's tired or hungry. the stores with all their colorful labels, bright lights, & noise can be overstimulating.