What you have posted is what native speakers would write. You could make it read more smoothly if you were to write "I was on my way to visit my parents last night when the elevator in their apartment building failed, and I was stuck in it." but that's a suggestion, not a correction. If you were writing in UK, as opposed to US, English you would write fuel, or petrol instead of gasoline, motorway instead of freeway, lift instead of elevator and block of flats instead of apartment building. You have an absolute right to choose which dialect you prefer!