I agree, probably a sore hock. Of course, the urine could be aggravating it too. I doubt it caused it though.
As for the urine soaked fur, there are several things that could be wrong. She could have a UTI, which is making her have to pee a lot and miss the box. So I would definitely have that checked out first to make sure. Another possibility is that she could be developing arthritis, which can start when they are as young as 5. If it’s painful for her to get into the litter box, she might be peeing on the mat and then sitting in it. There are some things that can been done to help with that. But you’re going to want to make sure that’s what it is and not something more serious. Do you have a good vet?
In the meantime, you could try using cornstarch to soak up some of the pee in her fur. A butt bath is okay, but you don’t want to do it a lot because it can cause the skin to become irritated. If you use shampoo at all, it needs to be something with no dyes or fragrances and is hypoallergenic.
Here’s a nice article on it: http://www.bio.miami.edu/hare/buttbath.html