My older daughter plays the violin, and my younger daughter wants to start. Is it okay for sisters to play the same instrument?
The short answer to this question is, yes. Siblings can play the same instrument. There is, after all, no law prohibiting it. The long answer would be, that it depends. It depends a lot on family dynamics. In some families I have taught over the years, every child played the violin (sometimes a pair of siblings, sometimes more). A few siblings took it very seriously and practiced a lot, other siblings did not. As a result, sometimes the younger students played at a more advanced level than their older siblings and no one seemed to mind. In contrast, I have known of other families who considered an instrument to be "taken" once one sibling had begun study on that instrument. Younger siblings were allowed only to choose an instrument that no one else in the family was playing. The reasoning being that when siblings are playing on the same instrument, someone is bound to have an easier time learning/excelling, and it is not always the sibling who is the most passionate about the instrument. Said parents did not want any kind of musical competition to interfere with the relationships between the siblings.
The question for you to ask is what the dynamics are between a specific set/group of siblings in your family. As the parent(s), you are probably in the best position to judge wether having siblings playing the same instrument will be "harmonious" or not within your household!