Puppy and older dog

My 3 month old lab puppy will run after the ball when my older lab (who has had hip sugery) is playing fetch. She thinks they are playing together and will grab the ball from her.I can keep them separated when we are at home, but as they grow older and they travel with us or go to a dog park, i won't be able to do this. Is there any way to train her to know when the ball is for her and when it is for her sister?

If you throw it for your older lab, then hold the puppy back or use treats to keep her from chasing the ball. However, it's going to be really hard to teach her to only fetch a ball sometimes, and especially with something as arbitrary as throwing it for another dog.

You might want to link holding her back to a command like "It's for ________". In other words, say that command, hold her back and give her some treats, and throw the ball for the other dog. Make it a positive thing, and the next time you throw the ball say, "Its for you!".