A UTI - urinary tract infection - can make cats (or humans) feel like they have to "go" RIGHT THIS MINUTE. And they do...Jill, if she has one, might just poop at the same time.

You can try Feliway to calm her, and Nature's Miracle to completely deodorize the area.

There are people here on PT who know really good animal behaviourists.

Jill sounds like she might be happiest as an only cat. Maybe someone here can help find a home for her.

hugs
Catty1