Your child is overseas behaving poorly, but your concern is with your adult friendship? I think the focus is in the wrong place.
My concern here would not be with the adult friend.
My concern would be my own daughter and whatever behavior she is picking up from her "god-sister" as well as behavior she is showing toward her aunt and grandparents.
I think your sister either is a total saint or had zero idea what she was getting into by taking two teens into her home. She probably expected a minimum of respect. But both girls can say, "You're not my mom" and carry on with the behaviors.
I would reel my child in. Overseas stay is done. She has to earn her time abroad by behaving appropriately while there, and she isn't doing that. If it were just her, alone, you would have more of a shot at long-distance threats and saying "One more chance" but I think having two of them there together means your authority from so far away is undermined; she has her buddy there and they support each other.
If you are still worried that pulling your child back home would hurt your friendship with this other mom -- please, reconsider your priorities.
I am surprised your sister has not told both you and the other mom, "We're done and they need to come home now."
ADDED after SWH: I did see that you set boundaries for your kid but how can she realistically "run everything by" you from another country? As long as she and her friend are there as a pair, your daughter is going to be torn between what she knows, as a basically good kid, that she should do, and what she feels she should do out of friendship and loyalty to her peer. If there were not another teen in the mix here, that would be different. But unless the other girl gets reined in or sent home, I would worry that my daughter was conflicted by her presence. Your child should not lose an opportunity because of her friend's behavior, true. The best solution would be for your goddaughter to come home, frankly, and let your child be with her family overseas.