Can I use homemade vinegar dog urine recipes in a Bissel carpet extractor?

I've read online about several home made remedies for dog urine odors in carpet. My bedroom smells! I have 2 shih tzus. Most remedies say use a white vinegar/water mixture and soak it into a "stain". Then blot it up with rags. I want to do the whole room, not a "spot". Then a 2nd step involving hydrogen peroxide and dish soap. I have a Bissel carpet cleaning machine I bought for about $150 that holds about 1 to 1 1/2 gallons of cleaner/water. I've tried many types of solutions from walmart, still smells. Does anyone know a way to use the above products to mix up gallons of fluid to do a whole room with a carpet extractor/shampooer? Or, can I dump a bunch of vinegar/water mixture on the carpet and use the empty extractor to suck it up? Will using the tank empty on the carpet machine ruin it, or will it just fill itself with the white vinegar/water/dirty pee odors? If you have another idea(s) or recipes please write! Thanks.