Well, I understand you!
I have dogs and I know how we care for them (as so as they do for us)
Perhaps you can rent a vacational apartment for a week or some days in webs like “Niumba”, “Rentalia”... I’ve used them so many times.
I am not friendly with the idea to rent a permanent house without seeing it before. I have to see it, what condition is it. For example, if you rent an apartment which is very noisy… In pictures you can’t know! :s
There are also so many “hotels for dogs”. I am not able to recommend any because I don’t live in Madrid, but it could be a great idea while you are searching a home. You can plan many appointments with agents before you are coming.
Once time I went on holidays without having nowhere to stay, me & my boyfriend went to the real state agents with our dog. It’s a way to assure that you can have dogs there and he’ll like his new home XD I know this isn’t the way to go, but our dog was a puppy and we were worried to let him alone at car, or renting a place online where he couldn’t stay in the balcony because he could fall down, etc.