Litter Box Training for a kitten

We just adopted a kitten a couple of weeks ago - she's about 9 weeks old. Her litter box and food is in the basement, and we made a little door in the basement door for her to go through to get down there. We originally had the litter box upstairs and she was using it without any problem, and then we moved it, and again, she seemed to be using it. I have seen her several times peeing in a corner of the basement, away from her litter box. I sprayed the area with cleaning products to get the smell away, but she continues to go back to the same spot, even when I tried to block it off. She also keeps peeing on my dog beds....I have 2 dogs and 2 beds, and she will just squat down on either one and go. I've cleaned the beds and gotten the smell out. Any time I see her peeing, I bring her to the litter box to show her where to go. Am I doing something wrong? Should we bring the box back upstairs??
TIA!

Re: Litter Box Training for a kitten

My instinct would be to give her two boxes for now. One upstairs and one down. She might eventually like the one downstairs, but at least she will be successful with it upstairs again.