Will a sanitary cut on my yorkie puppy prevent "stool sticking" ? Or will she still have the problem?

She's on dry puppy food, & her stool is not "sticky" really when I clean her, it's normal, just getting "stuck" in her hair around behind area. She didn't have this problem first few days I had her, but once it happened once, it seems to happen everytime now. And it's a nightmare! I walk through my house & find doggie poo all over the floor in small pieces or "skid marks" I'm going to call them (lol) where she drags her bottom on the floor trying to get it off. My house smells like dog feces, & she smells pretty horrible herself if you can imagine. Her hair is kind of long in that area, should I attempt shaving it? Or just take her to the groomer? Will a sanitary cut keep this from happening, or is this just something I'll have to get used to owning a yorkie? I don't want to shave her behind if it won't grow back, but want to put his problem to an end QUICK!