When we introduced my cat to my fiance's senior cat, his cat did the same thing. She'd chase my cat whenever she went to use the litter box, and whenever she felt like it. So my cat stopped coming out to eat or go to the bathroom because she was so scared it'd happen again. I tried getting Poppy(my fiance's cat) to stop it, to the point I'd hold her down whenever I saw Cookie(my cat) peek her head out and see if it was safe, but I could never catch it happening all the time. I wound up having to block off underneath the bed so my cat couldn't get there. Well, then she found high places to hide; and I wound up having to put a litterbox on the floor next to the place she was perching, and she'd come down real quick to use it, then pop right back up to her hiding place. Eventually I wound up cutting off her access to the perch, and left her with only one hiding place : the last shelf of the bookshelf which protected her on three sides, like she wanted, but left her with little space to stretch out and really get comfortable.
It was cruel, yes...I hated doing it. But it eventually worked. And she started coming out and going to the litter box, and stood up to being chased.
It takes a while. My cat would always give in and run away. But when she learned she was all out of options(and I hated taking away her safe places), she began standing up for herself. Now whenever she needs to use the litter box, she just does it, and ever since standing up to Poppy charging at her became mainstream, Poppy no longer has any interest in doing it.
Honestly, I think your cat is just testing your other two, like Poppy was doing with Cookie. I think she wants to find out what their boundaries are, and is trying to push it. Cats are incredibly intelligent - in a way I think Poppy helped Cookie gain more self-confidence about herself.