The name Home Sweet Home in Chinese / Japanese...

This means “Bless this house” or “Bless this home,” in Japanese.

Some may also translate this as “Bless this family,” since the Kanji for home can also mean family.

Note: Because this selection contains some special Japanese Hiragana characters, it should be written by a Japanese calligrapher.

福宅 is perhaps the Chinese equivalent of “This blessed house” or perhaps “home sweet home.”

This phrase literally means “Good fortune house” or “Good luck household.” It makes any Chinese person who sees it feel that good things happen in the home in which this calligraphy is hung.

四海為家 literally reads, “Four Seas Serve-As [my/one's] Home.”

Together, 四海 which literally means “four seas” is understood to mean “the whole world” or “the seven seas.” It's presumed to be an ancient word from back when only four seas were known - so it equates to the modern English term, “seven seas.”

This can be translated or understood in a few different ways:
To regard the four corners of the world all as home.
To feel at home anywhere.
To roam about unconstrained.
To consider the entire country, or the world, to be one's own.

在家千日好出门一时难 is a Chinese proverb that literally means “At home, one can spend a thousand days in comfort but spending a day away from home can be challenging.”

Figuratively, this means “There's no place like home,” or roughly a Chinese version of “Home sweet home.”

故郷忘じ難し is a Japanese proverb that means “there is no place like home” or “home is sweet to an exile.”

Note: Because this selection contains some special Japanese Hiragana characters, it should be written by a Japanese calligrapher.