A picture of the set-up, especially when soiled, can be helpful for members to give specific suggestions.

Generally, the bigger the litterbox, the less likely peeing/pooping outside will happen. As rabbit owners, we need to remember that the actual structure/perimeter of a litterbox is only meaningful to us humans– there’s nothing in the nature or intellect of a rabbit that tells them, “Ah I should just go inside of this random object”. It sounds like she is peeing around the area of the litterbox, which for many owners is actually categorized as a win in litterbox habits, haha.

There are some litterbox training strategies outlined here: https://binkybunny.com/infocategory/litterbox-training/

Can she access hay from outside the box? I had one bun that I had to be very careful with hay rack placement, because she would sit outside the box and eat hay, and just pee where she was.

It worked for me to use a hay rack, and hang it so she could only reach it once she was sitting in the box. It was kind of tricky to place it, but it helped a lot!

For that one corner of the rug, it sounds like that’s where she either likes to pee and/or it’s not fully cleaned there so it’s been deemed a place to mark and go consistently. We need to negotiate a bit with rabbits so simply more boxes in these locations might be needed.

I had a bun that kept remarking an area of carpet, and if I blocked access she would pee next to the barrier. 🙄

I had been cleaning it with a vinegar solution, and I realized it was starting to smell really strongly of vinegar, so I think she was actually marking because of the vinegar smell. I finally cleaned it really thoroughly with a carpet shampooer and nature’s miracle carpet shampoo and she stopped marking the area!