Who is more deserving of care and rights: the wife and immediate family, or a sister who has no one to support her? What is the evidence for this from the Quran and Sunnah?

Both the wife and her family, and the sister, have rights over the husband and brother respectively. For the wife, her rights over her husband include good treatment and companionship in an honorable manner, as Allah Almighty says: "And due to them is [reciprocal] good treatment just as due from them." The wife's family has the right to respect, good treatment, and benevolence. The sister has the right to kinship ties from her brother, kindness, and the obligation of financial support if she is in need. It is obligatory for a Muslim to fulfill every right due to its owner without neglecting the rights of others.