That could get very frustrating! I think I have a different view than you, so not sure how helpful this will be, but I tell them their bottom isn't a toy and to stop playing with it. But i never refer to it as a bad thing or anything. I don't want them to think it's a bad body part. If they are looking and learning about it, it's different. They have the right to learn about it, but if they are using it as a toy, I'll just say "Your bottom isn't a toy. It's special and you need to stop playing with it."
My kids have never been as focused on it as your daughter is, though! So, I can't speak from experience in how to stop it.
Oh, another thought, if she has ever had antibiotics very much in her life, it could have messed with her balance and it might be making it sore and itchy (though, like you said, it's also very much likely due to being bothered so much from her touching). But you might want to try some type of probiotics for a while to help balance it back out. I get yeast type of reactions easily, due to antibiotics in the past, and probiotics help. I'm not sure if mine ever looked red or infected when I was little. Just that I had lots of discomfort from it when I was younger too.