I’m not clear on whether your daughter has an autism diagnosis, but fecal smearing occurs with both typically developing children and those with autism. This is also something that can be effectively treated. In my experience this is much easier to treat using positive reinforcement than using punishment or guilt. I would recommend sitting down with her and coming up with a plan. Make sure that she understands that you’re on her side, that this is something that it isn’t ok to be doing and that you want to work with her on it. Children do many things that they know are “wrong” or that people might think are “disgusting” even when they know they shouldn’t and they often don’t entirely understand why they’re doing it.
Rather than using punishment, I suggest arranging special reinforcement for her if she doesn’t touch her feces or do any smearing. Perhaps a special treat after school or some activity that she would really love, watching a movie, spending time on the computer, whatever. If there is a smearing incident, don’t make a big deal about it, just move on and she can try again the next day. Reserve the big deals for when she does something great! This is something that you and she can work on together and something that is very amenable to treatment using positive reinforcement.
I came across this and it may be helpful? Good luck to you.
"The practice of smearing feces is clinically known as scatolia. When not associated with psychological impairment, it manifests when an individual faces extreme powerlessness and frustration -- instances in which an individual believes that his rights have been wholly stripped, and that the entire system is conspiring against him. He wants to communicate his frustrations, to lodge his protest, but he believes that the system has even assimilated his protests..."
Have you talked to her pediatrician? There must be something that causes this behavior. Perhaps her Dr. can reccomend a therapist.