Oh, boy three dogs, that's going to be a problem with any sort of hardwood floor. That's a bit of a dilemma also, because the only finish that just might stand up to the claws of three dogs would be found in the polymerized titanium coating found on the expensive Lauzon hardwood floors http://www.lauzonltd.com. But then of course there is the problem with the many seams with prefinished and the pee will certainly go right between the boards. Urine will cause a stain on edges of the boards as it seeps into the wood. You could try to install such a floor and then apply at least two coats of an industrial coating on the floor before you even use it.
Go to http://www.basiccoatings.com and check out their Tycoat recoat system for prefinished floors. This is just about your only (expensive) option for getting their very durable Street Shoe coating to stick to this prefinished flooring. And even this is doubtful. But if this system works you would have the best of both worlds, and the two coating would seal the many open seams.
The other option would be to choose a narrow 2 1/4" red oak or white oak strip floor and sand and finish it on site with a dark stain and at least 3 coats of an oil modified polyurethane. The dark stained wood will hide any future urine stains, and the 3 coats of poly is still the longest lasting most water resistant coating we have. Some of the new water and solvent based industrial finishes on new floors are problematic, in that they will cause the new wood to stick together and possibly panelize. And they are in general expensive and somewhat toxic to use (including Street Shoe). At least the oil based poly is somewhat cheaper, and is more easily and cheaply re-coated in the future.
Water based finishes tend to turn white or opaque after 5-10 years, so their longevity is somewhat in question. And water based finished will give your wood and somewhat plastic look, especially over a dark stain. I only mention them in the first paragraph, as this Tycoat recoat system HAS to be used with a water based coating.
If you HAVE to have a wood floor, I would choose the darkly stained sand-on-site floor option. Just follow the guidelines in my Poly without the Bubbles article, and you will (with some care) have a floor finish that will last about 30-40 years.
Be sure to read the first part of my floor maintenance article to learn how to clean the wood floor safely. And you might check out the Cleaning Center's (web address in the article) DXO odor eliminator to remove any smells from the wood when accidents happen.
Unfortunately all these finishes will scratch, and you might be better served by a ceramic tile type of floor to be honest. Hardwood just might be more trouble than it's worth.
You may also find these articles helpful:
1. How to remove and clean various stains and odors from wood floors
2. How To Clean And Maintain Wood Floors PART ONE
3. How To Clean And Maintain Wood Floors PART TWO
4. Floor Types And Finishes
5. How To Take Care Of Your Health And Safety when Installing, Finishing, Repairing or Cleaning your wood floors