Our 3 dogs sleep & spend some time during the day on a long covered, weatherproof verandah room that runs the length of the back of the house. ( There are big glass sliding doors connecting it with the house).
We solved the 'going to the toilet' problem for the dogs by fencing a small area around the bottom of the deck steps.
There's a doggy door in the door leading down the deck steps. So when the dogs want to go to the toilet, they just go thro' the doggy door, down the stairs from the deck & into this small fenced area. They can do their business & go back up onto the deck without disturbing anyone.
There's a gate in that small bit of fencing so people can go down the steps, thro' the little fenced area, & out the gate.
Such a small bit of fencing was needed that it didn't cost much.