"Mom is in the kitchen."
I think it's acceptable, but it sounds a bit off. You should use נמצא instead in sentences with location, (X is in Y) or not use a copula altogether.
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So, I should use נמצא in the sense of "is located / situated in" like e.g. "הקולוסיאום
נמצא במרכז רומא" and only use the personal pronouns for emphasis, as in "רומא
היא עיר הבירה של איטליה", right?
No difference. Formally you're supposed to write אימא if you write without nikkud, but most people write אמא with or without it. So to sum up - both ways are OK and mean the same thing.