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Am I (29f) the asshole for insinuating my gf(29f) rehome her cat?

Am I (29f) the asshole for insinuating my gf(29f) rehome her cat?

My gf moved in with me two months ago. I rent a house (1000 sq ft), we have seperate rooms and my kids have their own room. I also have two cats and a dog. It's already a lot of people and animals for a small amount of space. She brought her cat with her and I warned her that there may be too many cats for the space and that they may not get along (as cats are territorial). She said her cat was confined to her room at her last roommate's house and would be fine just staying in that space separated. Her last roommate's place was very gross (untreated flea infestation for years, let their dogs pee and poop in the house and never took them out, etc) so I warned her ahead of time that I'm very sensitive to smells and really don't want cat pee in the house. I'm sure you can see where this is going.

My cats have actually been super friendly to hers and try to greet through and under the door. Hers not so much, but after two months finally seems to be chilled about it. This whole time her cat has been peeing on her stuff every few days. Ruining clothes, shoes, purses etc. I hate to think what the carpet is like there now. She's been letting her cat out and leaving her room door open more and more, especially when I'm not there to get her cat acclimated to the house. I'm extremely not comfortable with that, and already have found a pee spot by her door that smells awful. I insinuated this morning that that's not ok, and she's not going to be allowed to pee all over the furniture. She says it's because her cat is spiteful and just wants to be out where everyone else is, and is getting revenge by peeing. And that also means she's still adjusting to the new space. I'm not buying it and I'm not happy. I told her she needs to go to the vet for a UTI check and get some cat pheromone plug-ins to chill it out if she's going to keep it. I'm ready to say she just needs to move out with her cat, but really I can't afford the rent alone until I get a raise at the end of the year.

Am I the asshole for being upset about all this? Especially since the boundary was set early on?