This helps children remember the puppets' names so that they can address the puppets more easily. Puppet One snatches the ball. The puppets thank the children for their suggestions, and then animate various solutions. Children choose an acceptable one, and can see the advantages of a win-win solution. Ask the children if they can remember any similar conflicts they have been involved in and help them consider solutions that might have worked.
Adults can remind the children of the suggested solutions at a later time.
Your idea was that they could roll it to each other so they could both play. Affirm even seemingly ridiculous ones. Keep the action slow and take a lot of pauses. This enhances comprehension and gives the children time to put their thoughts into words. It also gives you a chance to hear everyone.