Marry and live in a border town in the US until she gets US citizenship. That's what we did.
A green card means permanent residency. One must reside in the US in order to keep permanent residency. In theory, the moment you move to another country to reside, you lose your US permanent residency status. But in practice it is hard to prove exactly when someone moves abroad to reside, since short visits are no problem, so the government applies some tests to decide. If you remain outside of the US for an entire year or more, then you lose permanent residency unless you obtain a reentry permit in advance. For absences of six months to one year, you are assumed to lose permanent residency unless you prove otherwise. Repeated absences of just under six months each may also trigger removal proceedings on a case by case basis, but there is no hard and fast rule for this case.
Once you obtain US citizenship, all the problems go away. US citizens keep their status for life unless they renounce it at a US consulate. Unlike in Canada, where a naturalized citizen must promise to reside in Canada (thank Harper for that), there are no restrictions on where a US citizen may reside.
