You explained yourself well enough, so don't worry about revealing too much.
Ultimately it might be best to "let the ship sink". There's only so much you can do here, especially regarding the situation with your family. It'll be hard, but you need to say something to everyone involved. Let your coworker know that her behavior bothers you. If it doesn't stop, report it to HR- what she's doing sounds like sexual harassment. Regarding your family members, sit down with them and have a conversation about cleaning. This shouldn't be your responsibility alone; everyone needs to contribute equally, and if they refuse to help then stop picking up after them.
There's always the option to switch jobs or move, but if you don't have those resources (and a lot of people don't) then there are other options you can try.
I guess I'm responding because I'm living with my parents and they don't make an effort to clean the house often, so I'm often left picking up the slack. They both work full time, and our home got flooded so they have an excuse not to. But it still frustrates me that it's become my responsibility. Reading this actually helped a lot: https://archiveofourown.org/works/28971924
I found that fic after playing Omori, and while it didn't solve the fact that our house is in the state it's in, it captured a lot of the frustration and misery I was feeling at the time, about my situation. So reading it was sort of cathartic in a way, if that makes sense.
Maybe I'm not the person you were hoping to get a response from, but my point is, people do care, and they are willing to help. It just depends on who you reach out to. I'm sorry you're forced to put up with all this mess, anon. Hopefully things will get better.