Thought to chew on, from a dispassionate financial-wise perspective on what to do bigger picture when the only option is to accommodate the loved ones and their loved ones. The instinct to go with option three is a good one. Unless the dog was gone today, even if the carpet cleaning did work, it's still at best a temporary solution that will still persist and increase the odds of further urine damage to sub-flooring and yadda yadda long term.
The dog's not going anywhere anytime soon it sounds like, so trying to salvage the carpet no matter how new seems like a losing proposition for what has effectively become a room-sized absorbent elderly dog diaper. You've had the carpet less than a year, and despite two months of successful diaper usage before the cagey little scamp worked out an escape? You're already having to resort to professional cleaning for the smell, which although cheaper than new flooring, still isn't cheap, and will be harder to have succeed every time you have to have it done (if it even succeeds the first time), which is already on track for needing to be done at least once a year or more over the next three years with building layers of funk between cleanings that will only compile until you go nose-blind or reach your tolerance level, whichever comes first.
If you're able bodied and capable? Cut your losses and write off the carpet now. Interlocking, water-resistant, cheap LVP flooring might be the superior, cheaper option long term, and will give you access to use enzyme cleaners on the subflooring now before it gets too bad/too much long term, and gives you an additional opportunity to put down a plastic barrier underneath as well. You could probably do it for as little as about $2.50/sqft., and save any good flooring down the road for a time when maintaining good flooring will be... less challenging.
The things we do for pets, sometimes.
Just my corroded two cents worth. Take it for what it is.
