The question isn't whether she is permitted. The question is whether the green card improves her chances. See the first post.
Lots of countries claim my wife can visit with or without a green card, but they lie in order to seem progressive. What they say and what they do when she applies are two different things. As an African, you should know this. Europeans do things like rejecting famous African university professors who want to attend conferences. They think every African, no matter how successful, will refuse to go home.
I respectfully request you not try to shame me for criticizing dreary vacation destinations. Paris is nicer than Manila. Switzerland is nicer than Tanzania. Everyone knows this. Nothing wrong with pointing it out. Laying guilt trips is not nice, especially when you, yourself, are choosing to leave the kind of place I'm talking about. And I'm immune to guilt trips anyway. It is not possible to make me feel guilty when I'm right.
If you're trying to move from a poor country to an affluent country, it makes no sense to try to shame other people whose preferences are just like yours.
Everyone here is trying to move someone to a first-world country. There is no backlog of Americans and Europeans trying to move to poor or oppressive countries. No one here has room to criticize others for preferring pleasant places.
My wife has no interest in visiting other African countries. After all, she has been in Africa her whole life. She has never traveled before, so she wants to see the rest of the world, and I want to make her dreams come true. She isn't dreaming of Africa or unpopular spots like Ecuador and Albania.
As for the Caribbean, I don't like it, and I don't want to waste our precious times together there, not to mention thousands of dollars. I grew up in Florida and spent a lot of time on the water and boating to the Bahamas, and I live in a warm place now, so I have had enough of the hot, boring tropics for a lifetime. She doesn't want to go to beaches, either. She likes places that offer intellectual stimulation. Also, flights to the Caribbean are unbelievably long and expensive. The airlines are not working hard to help Zambians get there.
Mexico is also a difficult place for her to fly to, and when you get there, it's like where I grew up, only poorer.
We are shooting for a Schengen visa through Czechia, and if it works, we'll use it to get into Austria and Switzerland. If not, we are stuck with Hong Kong and Singapore, which aren't too bad when the weather is good. By the time we find out about the visa, at least the monsoon season will be over.