Grammatically correct response would be:
"In what restaurant are you eating?"
But a more natural sounding choice of words would be:
"In which restaurant are you eating?" (or 'sitting' or 'waiting')
or (more informally)
and even more informally
"Where?" or "Where is this restaurant?"
The first version your mother asked is incorrect because for some ridiculous reason, the rules of English state that it is not acceptable to end (have as the last word) any sentence with a preposition (sometimes called an auxiliary verb, and sometimes called a helping verb) and the word 'in' is a preposition.
Other prepositions are:
I think there are a couple more that I can't recall at the moment.
Though, keep in mind, that many native English-speaking people get this wrong all the time and it is a commonly and easily forgiven technical error of minor importance (in my opinion).
A Writer's Reference - Fourth Edition
A prepositional phrase begins with a preposition such as at,
by, for, from, in, of, on, to, or with and ends with a
noun or a noun equivalent called its object.