Cat Peeing Everywhere Since Getting New Kitten?

My grandma has a cat that she has had for years. She's fixed and is also an outside cat. Recently I adopted a kitten for my daughters. It was going all right at first; my grandma's cat would just hiss at my kitten and just avoid her when they are both inside. I have caught them actually playing with each other when they are outside.

My kitten is not fixed. She also has her own litter box and food downstairs and my grandma's cat has her food and litter box upstairs. I thought we were doing things right, but now my grandma's cat is peeing everywhere upstairs, on couches, floors, clothes, everything. I don't know what to do. Any advice please?

By Isabel