Is it permissible to leave one's divorced mother and siblings in a non-Muslim country and return to live in a Muslim country, while fearing the commission of a sin by abandoning them?

You have made an excellent decision to return to your Islamic homeland, given the corruption of faith and morals prevalent in non-Muslim lands. If your family insists on staying, then remain with them if you are able to perform your religious rituals and do not fear temptation, until they are convinced to return or you are no longer responsible for them. However, if you fear for your faith from temptation, or you are unable to perform your religious rituals, then you cannot remain. Take with you those who obey you, and leave behind those who oppose you, just as the Companions did. The evidence for this is the hadith: "Return to your parents and keep them good company." This only applies to one whose faith is safe in their location. But if one fears for his faith, it becomes obligatory for him to flee with it.