The living room idea is good. The processing of resources would be done most efficiently outside the Earth's gravity well (unless the resources to be processed were sourced from the surface). The slave labour idea has some merit though. Maybe the aliens have some kind of ideological opposition to using robots?
When it comes to resources like hydrogen it all comes down to cost-benefit analysis. Space itself contains lots of hydrogen - its just spread very thinly. But with technology such as an electromagnetic scoop it can be harvested very efficiently. The Bussard ramjet is an excellent example of a theoretical spacecraft design that uses this concept for fuel and propulsion. The Red Dwarf is a Bussard ramjet spacecraft.
In any case if you are talking fuel for fusion reactors, helium-3 is the way to go, not hydrogen. Helium-3 isn't something you can efficiently mine on the surface of a planet such as earth, the best places to get it in our solar system are from the solar wind, from the regolith of zero-atmosphere bodies such as the moon, or from the atmosphere of gas giants.
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 "It is better to be feared than loved" - Nicolo Machiavelli
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