You will need to get a professional cleaner to remove the urine. Hopefully, you can also get an enzyme spray that will help neutralize the smell. Invest in a non permeable cover for your mattress, since your pet may repeat the action.
Your perseverance in trying Pine Sol and so on is admirable. Using a mix of white vinegar and water to wash and rinse using a clean rag, will help remove the odor. Somewhat. At this point, it may well be worth trashing the mattress, and getting another. The odor is never really going to go away, since the urine isn't just on the surface of the mattress. If the problem is going to continue and you don't want to change mattresses, put a thick vinyl mattress sack on it after cleaning and airing as well as you can. Then, use a mattress pad--get two so they can be washed. Perhaps also add an additional rubber pad under the sheet if there is a commonly used spot.
You can purchase urine burn remedies for grass at your local hardware or pet store. Odor is a bit more difficult to remove. You can rinse your yard with a hose after your dog urinates. To remove urine odor for your deck, use a mixture of Mule Team Borax and water, or use a urine odor remover from your pet store.
In all my years of owning cats and having to deal with these issues, removing cat urine from a mattress is the hardest. Since the usual methods of removal involve blotting the urine up and then spaying with an enzyme product, blotting again, then repeating that step and then placing a towel (paper or cotton) over the area and spray that with the enzyme product every day to keep it moist and activated, it is a little hard to then use said mattress. Also, since the mattress is so dense, the urine soaks deeper into the mattress the more layers of moisture you add to it, do you may mask or eliminate the odor from the surface of the mattress but to tell you that you will get rid of it totally, I don't think so and I'm pretty sure that your cat won't either, they will still be able to smell it deep in the mattress. I have never tried the cleaning process stated above and then flipped the mattress so that any moisture will come back to the surface instead of sink deeper into the mattress. Try it and if it works, let me know. Otherwise, pitching the mattress may be your only option.
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