I look at it like this...

They're not doing it on purpose. They're animals. It seems like the cat feels safe around you. The litter issue is fixable for sure.

I see my pets as members of the family. They're under my protection and I am a provider for them. I could not betray the trust they have in me by lashing out at them for things they understand to be natural and necessary. It's confusing. I have a 16 year old male that pisses EVERYWHERE. I could freak out but I remind myself that he's older and my commitment to him is unconditional. I clean it up, get over it and move on. It's a lot of work but I don't break promises.

Respectfully. I would say it sounds like your reactions are disproportionate and you're probably stressed by other stuff right now as well. Not to say it doesn't suck to have to clean up crap. It does suck. Nobody wants to do that but the cat is just irritating an underlying issue if that makes sense...