Cats can really have a bad odor and most owners are unaware since they get used to the odor of the cat. Cats spray carpet, furniture, clothing, walls ect…
If you had to choose who keeps the home, you and your kids or the Cat… Who do you choose? Is the Cat worth losing your home? As for the Landlord, avoid argueing and any confrontations. Lose the cat if it will resolve that issue with the landlord.