I think it's idiomatic in English "in the home" (implied in my/our home) -> "at home".
"In the home" could be used in English, but with a different meaning, meaning "in the house" E.g: "I left my keys in the home" = inside the house.
According to the example they gave on Stackexchange, "in the home" could be also used here, in this sentence. (They sleep in the house, inside the house.)
But I really think that "domi" is always best translated with "at home".