You have a tough, nasty job ahead of you. The carpet should come up OK, but the rest of the project… Is there anything between the ceramic tile and the linoleum, such as plywood underlayment? Or is the linoleum (I’ll bet it’s actually vinyl)glued directly down to the tile beneath it? Whatever the situation, if your floor is on a concrete slab, you will have a very labor intensive project ahead of you. After the carpet is removed, you will have to pry up the tack strips around the perimeter of the room/s. Then the sheet flooring will have to be peeled back from the tile below it. Now the real fun begins. The ceramic tile and the adhering morter will have to be chipped and chiseled up from the concrete floor. This can be a very hard project to get the floor smooth enough to be painted, if that is really what you wish to do.

I wonder if the urine smell isn’t primarily in the carpet and padding. If that were to be the case, you could save yourself an incredible amount of difficult labor by just ripping out the carpet & pad, cleaning the linoleum thoroughly and installing new pad and carpet.