Hi Optimist, just a suggestion, but why not just cover up the floor again? Vinyl flooring is easy to clean and won't let the leaks through to the wood underneath. Much easier to install than all that refinishing, plus it's easy to take up again if you want to change it someday. Pay a visit to a flooring store or even a big box store, you might be surprised at what's available. Most places will give you a free estimate on installation, maybe something to consider. Save a little piece of the old carpeting, you might be able to get the dogs to transition from that to newspaper or "pee pads".
Shelters in Arizona are full of Chihuahuas, anyone looking for a rescue?
Dogs