Help! Dad wants to lose one of our cats?

She needs to go to the vet. Cats are very clean, and only go out of the box if it's too dirty for them or if there is a medical issue. How many litter boxes do you have? There needs to be one per cat. Does she have to go down flights of steps to get there? Painful joints may be preventing that. How do you know there is "nothing wrong with her". Did the vet tell you that or are you making a guess? She isn't stupid - she is trying to tell you that something is wrong in the only way she knows how.

Taking her to a shelter is cruel. If you aren't willing to take her to the vet to be checked out, then do the right thing and take her to the vet to be euthanized. The shelter will do that and then she will die alone and afraid surrounded by strangers. No one adopts a 13 year old cat with health issues.

1. She is doing this either because of age where she can't control her urges, doesn't feel like traveling to the litter box or finds the litter box too difficult to climb.

You can try using a shallower litter box and place a few close to places she poops and pees.

2. She is too old to adopt and will definitely be killed in a shelter. Leaving her is as good as killing her so know that and let your dad know that too.

3. Help your dad more. Clean after her like any young one in the house cleans after their grandparent if needed. Old age is real and all of us will go through this. Let her stay and improvise

How many cat boxes are available for the cats to use? How often is the cat litter changed or the pan itself being washed and sanitized?

If she is declawed, maybe the litter hurts her feet and you need to find a well ground litter, like Nature's Miracle. And getting the multi-cat clumping litter helps.

When was the cat last seen by the vet? Has the cat been checked for a urinary tract infection or possibly an anal sac infection? And maybe the cat has internal parasites.

Just stating firstly, your cat is not stupid, please don't assume just because it might have something medically wrong with it it's an ignoramus. Your cat may have a bladder/kidney problem/infection or may have some kind of disease. If not it may just be spraying from territory issues. My cat has spraying problems and we kennel her in a large kennel and she no longer sprays. Take your cat to the vet and make sure it doesn't have a problem. Just because it seems like cats get along doesn't always mean there isn't a problem, that's what happened with my cats. Please take your cat to a reputable vet immediately to ensure the best health to your pet.