You apply for reentry permit for her that will enable her to stay out for up to two years.
She still has to maintain residence in the sense of paying taxes, etc
You are welcome to contact me if you wish to discuss your case further.
Yes she can stay out longer with a reentry permit, however, there is a limit to the nubmer of reentry permits they will issue. When someone applies for a green card, they are stating that they intend to immigrate as opposed to visiting. Since they have taken up a number out of the annual green card quota from a person who maybe did intend to immigrate, the authorities frown upon people getting a green card & then not living in the US. As for your question, yes, she can go to the US Embassy in her home country & inquire about surrendering her green card, but its my impression they are not giving 10-year visitor visas anymore. But I'm not sure about that.