Is it okay to return a kitten (brought privately) to the same owner the next day?

Your parents should have your sister contact the original owner of this kitten IMMEDIATELY and explain the situation. Then, at least, even if you have to wait until tomorrow to return it, the original owners will already be aware and prepared. Also, since your sister purchased this kitten after being told NO, she shouldn't get a refund on the purchase price. Sometimes when people do things like this, it's a good deterrent that they should have to face some consequences beyond having to return the pet.