Interveiwing at home, their home I would say that this is the normal.
I know full well that Minster Cleaning yes the big franchise does this exact thing "Interveiws them at home".
Although I think its a good idea and yes if the place is clean then I would say they would do a good job. But I also know I have staff that their cleaning is "fantastic" but their home is a complete mess. They dont have the time to clean it. so they tell me.
As for interviewing at starbucks well thats down to you, We use an office that we rent. Or you could rent a room "An office room" You can rent them by the hour. Have a look for virtual offices in your area. They even greet memebers in your company name, bring tea and coffee, supply fax, email etc.
Also as for covering work until you find a cleaner, this is perfectly normal I have found this with many companies.
Dave