I am so sorry that you are having these problems with Kate. Now that she is on anti-biotics that should take care of her problem. I had a similar problem with Emily and she peed on my goose down duvet. Once I took it in to be drycleaned I never had any problems. So regarding the furniture, take any cushions into the dry cleaners and that should get rid of the smell.

Once the door is hung on the basement you might want to consider treating the basement floor. I assume that you have a concrete floor ... treat the area that the animals use with the odor remover. Once that is dried, wash the entire floor and wait for it to dry. Then seal the floor. You can buy the sealant at Home Depot or any hardward store. This will prevent any water (or other liquid) from penetrating the concrete (also handy with floods). By doing this, it prevents the smell from penetrating the floor. If the animals do use the floor again, the smell won't penetrate through the sealant.

Good luck and please be patient with Kate, so had no other way of telling you that she was sick.