I agree with Sherri. Keep her on a leash, and attach the leash to your belt or something. She will be happy to be near you, I'm sure. And then she's sure to let you know when she needs to potty (either whining, pacing, trying to get away to go to one of her "spots").
And your daughter is likely correct here. Punishment like that is not a good idea and will lead to other habits to get around that. Only if you catch her actually pooing, then you can make a startling noise and move her to the correct location.