"Their home is in Brazil."
Translation:Ilia hejmo estas en Brazilo.
In English house is a physical building used for habitation, such as a stand alone building with two bedrooms and three baths. An apartment isn't a house. A office isn't a house. A jail cell isn't a house.
Home is a logical construct that means, "this is the place I go to consider myself at rest from the world." It could be a building (middle class), alley (homeless), jail cell (incarceration), work (as in that person is more comfortable there) or a mansion (a gigantic residence, too large to be considered a house in American English). Wherever it is, typically it's understood to be singular, as in you have exactly one.
"I'm going home", makes sense as it's implied there is one.
"I'm going to the house", means some specific house, maybe one you are building. Notice an article is necessary.
"I'm going to a house", could be used if home shopping.
House shopping is something a landlord does, as they have no intention of living there.
You could use it and would probably be understood...there's 20,000 hits for brazilujo on Google. But should you?
I found this from Claude Gacon on the influence of Volapük on Esperanto:
Fakte Britlando kaj Brazillando estus logikaj, sed Brazilujo estis vera idiotismo, tio estas peko kontraŭ la logiko de la lingvo mem. Britujo povas konveni, ĉar oni povas imagi ujon, kiu entenas la britojn. Sed oni ne povas imagi ujon, kiu entenas la teritorion Brazilo.
(all mistakes mine)
In fact Britlando and Brazillando would be logical, but Brazilujo was a true idiom, it is a sin against the logic of the language itself. Britujo can be appropriate, because one can imagine a container, which contains the British. But one can not imagine a container, which contains the territory Brazilo.