Ok…so you are married to a U.S citizen.
I agree with others. Do nothing to make anyone question why you got married. Don’t let this look like a marriage ONLY for the purpose of gaining citizenship or green card status for college. Just don’t.
Plus…you and your wife don’t have enough income to support living separately.
Why can’t you go to college within commuting distance of HER parents home to save money? Live together there.