If she does not have a green card or US passport, then you must mark on your tax return married filing separately. You have to show your married status correctly not to have problems later. Even though you mark filling separately, she does not need to file until she gets a green card or passport.
they recommend not getting a green card until you both plan on living in the states. It will only make her exposed to global taxation. And you don’t need to worry about the green card abandonment issue.
She should be able to get a one year multiple entry visa every year without much trouble after the first one.
