I've known a couple of moms who had their children clean up after them to 'teach' them. They were so desperate to try anything by that time. They were much older, both 5-6 years old.
But for a three year old who has very recently learned to potty train... the whole cause/effect (Mess out of potty -- clean up on my own vs. using potty) developmentally, it's much too old for her to understand. It's really really harsh for her and it could set up a control battle you definitely don't want to fight. Nasty, prolonged, and very yucky to you both.
I don't know how old in her 3 years she is (closer to 3 or closer to 4) but a body does not have full sphincter control until just past 36 months. Even then, it's a lot of courage & coordination for a young child to face that loud potty every time to give up something that's part of their body, no matter how us adults view it.
A really helpful book on potty training that helped me to understand the mental & physical process a child goes through for Potty training is:
No Cry Potty Training solution by Elizabeth Pantely. She's very good at explaining how potty training is a long patient process instead of a skill gained immediately.
My dd gave up diapers in the middle of January. Biologically she was 3 years and about 4 months old. We had a lot of conversations before we started about giving up diapers and pooping in the potty. It scared her even though she was eager to do it. She didn't gain full control until April or so. It took her until May to feel comfortable pooping on the potty instead of in her nighttime diaper first thing in the morning. And that was with a lot of positive reinforcement. Even when I was frustrated, I didn't show anything but a "Well, next time, let's do it on the potty." It was very hard sometimes to do that. She's great now, but I still consider the whole potty training incomplete and more like a work in progress.
You probably won't like my suggestion. Since she is only 3 and seems to not have ANY interest in #2's on the potty, put her back into diapers/training pants to give you both a break. Incentives do work like stickers or stamps or small cookies. But it sounds like currently, she has no desire to do #2 on the potty with you around. Give yourself a break of a week or two, then start over. It's better than cleaning up icky poop all over the place.
good luck