I looked at Annie's instagram and she has traveled out of the country since arriving to the States. I was under the impression immigrants weren't allowed to travel until they received their green card... Unless they ask for special permission (and usually that is in cases of family emergencies). So, I assume she already has her green card. Also, if you drive in the States as a tourist you drive with an international license, driving with a State license has residency requirements (aka green card).
Following on from the instagram posts, I have to assume their money issues aren't real, because they can afford to go travel and they went to the derby and Annie was looking really lovely. I think they've created a strange fiction to drum up some sort of fame.