All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Both the wife and the sister have the right to be treated kindly, so a husband has to balance between the two and should give each one her right. Fulfilling the right of one of them should not be a reason of neglecting the right of the other.
However, if it is predestined that there is a dispute between the two, then the husband should be wise in dealing with the situation and he should find out the reasons for such a dispute. He should endeavour to reconcile between them and be just in doing so, and he should repel the harm of the oppressor.
As regards declaring one's loyalty to a Muslim, it should be according to his obedience to Allaah. If both the wife and the sister are Muslims but the wife is more pious than the sister, then she deserves more love and loyalty than the sister.
Allaah Knows best.