help eliminate cat stains and odar

I've had my cat, Jeffery, for about three months now. I clean his litter box about every other day. (I only have one cat it doesn't seem to get too dirty) He pees everywhere though. I've tried multiple solutions such as, vinegar and baking soda, and shampooing the carpets, it doesn't seem to work. I also got another litter box to keep in a room downstairs. Yesterday I got a black light to see where these stains are, I marked the areas that he'd peed on and scrubbed with vinegar and baking soda, then vacuumed over it. After doing this, I shinned the black light again and the stain seemed to be gone.
My family wants to get rid of him, but I'll do anything to keep him. Do you think I should contact the vet? Any suggestions are very much appreciated.

Peeing outside the box is not normal. Your first step is always to contact the vet to make sure it's not an illness. Cats who experience pain of some sort while eliminating begin to associate the litter box with pain, and this avoid it.

Litter boxes should be cleaned every day at the very least. Does he use both boxes? What kind of litter? Where are they located specifically? Is it covered or non-covered? Have you tried different litters? How old is he (old cats are more prone to issues like arthritis)? 

As for cleaning, try an enzyme cleaner. Use the black light to find the spots, and use an enzyme cleaner such as Nature's Miracle to clean it. A cat's nose is extremely sensitive, and only an enzyme cleaner can thoroughly get rid of the smell.