I had an elderly cat who had similar peeing problems. We tried everything we could...confining, behavior mod...which didn't work. And we did medical testing...but at some point it just became too expensive to invest in extreme medical care for an old cat. In the end, we put her down. The vet really thought she was at the end of her life and probably couldn't be cured, so we felt good about the decision. Other vets might not be so honest and will take your money as long as you are willing to spend it.
My current cat is "only" 10, and when we got a new puppy last fall, she suddenly started peeing on the floor by the front door. I managed to solve the problem by moving her litter box to that spot. Now, she reliably pees in the box...but I have the unfortunate situation of having a litter box right inside the formal entrance of my house! Every time I try to move the box, she regresses to peeing on the floor again.
Cat pee is horrible stuff, and I don't think an incurable peeing problem is something many people would put up with. So, you're going to need to do what is best for your family.