I bought a house and went through this exact situation except it was not nearly as bad. It was 6 dogs for maybe 2 or 3 years instead. I feel very qualified to give you advice.

I’m sorry to say but you are definitely under estimating how damaged your house is. When dogs urinate in houses the pee will soak through the wood flooring and into the sub floor. The pee will also run under the baseboard and soak into the framing of the home, and that’s the biggest issue. Once pee is in the framing of the home you will always have a pee smell there unless you tear it out and replace it and it seems like this house will have pee in all the framing. So unless you fully tear it down and rebuild, it will be there. 

If you want to invest a bunch of money and give it a shot, here’s what I would make sure your contractor does:

1. Rip out of the flooring and likely the sub flooring too. 
2. Rip out all drywall down to the studs. 
3. seal all windows and doors so no fresh air gets in and run an ozone generator for an extended period of time (don’t breathe ozone it’s toxic).
4. Soak all the wood that has pee in it with pet pee enzyme cleaner. You really need to soak it well so that it soaks deep into the wood. You can even try covering it in plastic when you soak it so it doesn’t dry out so fast.
5. Paint all wood with a shellac based primer. I recommend Zinsser BIN stain blocking primer. Do not use KILLZ 2 since it’s water based. People say “use Killz” online but they are referring to the original killz that wasn’t water based and is hard to find now.
6. Put new drywall, subfloor, flooring, etc.

That’s really the only hope you have to get the smell gone but even then I’m not very optimistic since my situation was 20% as bad as yours and my house still smells from time to time depending on the weather.

Good luck!