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Domain would be the area their house is in, the territory they claim etc. The three desert houses share Dorne though for the most part. Affiliation are an organizations that they're part of and the strongest alliances they have with other Houses. So in the desert cases it would be both the others - except Martel, they have Lothian as well.

As the wife you can be anything so feel free to make something up if you want, just run it by me first.