"I am home" sounds wrong to me. I would say "I am at home".
Can an English native speaker verify this answer or reply to my comment to explain me why am I wrong, please? :-)
At doesn't really matter, for this particular sentence. I am home or I am at home, both examples are fine. "At" is an extra word, so we (English speakers) tend to drop extra words (or filler words).
Shouldn't ”Sometimes they're home” be an accepted solution?
Sometimes I am at home.