cat VS cat

i share a house with my older sister who recently got a new cat. the issue is that i already had a cat, who's litter is located in my washroom, while my sisters cat has her own litter but chooses to use my cats litter. and since my sisters cat started using my cats litter, my cat has been peeing at the entrance to the washroom, which i think is a way of sending a message to my sisters cat, 'stay out of my territory'.
what i would like to know:
is there a way to stop my cat from peeing?
AND how can i stop my sisters cat from sharing/using my cats litter?
i think i know what my cat is doing with peeing and sending a territorial message, but i hate having to scold her for it.

Your cat is stressed and upset at the arrival of this new cat, who has taken over her litterbox.

DO NOT SCOLD OR PUNISH HER IN ANY WAY, SHAPE OR FORM.

You are making her MORE stressed. I'm assuming you didn't do gradual introductions with these cats, so of course your cat feels "invaded" and probably insecure.

When cats avoid the litterbox, there is always a reason - at least to them there is!

Try putting both litterboxes in the bathroom and one more somewhere else. Clean them thoroughly every day, and try adding a few grains of each other's litter to the other's box after they have used it.

Also, take a towel and rub both cats with it, transferring their scent to each other.

Hopefully things will go more smoothly.