I personally wouldn't punish in this matter I would read the books How to Talk so Kids Will Listen, How to Listen So Kids Will Talk. And they have a sister book Sibling Rivalry. They have in them skills that work for teaching children how to resolve their own conflicts. For me the principles in the books seem to exemplify how several of our prophets seem to have parented their children the following comes to mind, others have said similar things about their prophet parents, but this is the most recent that comes to mind: The Whole Article is worth a read from this point of view.
LDS.org - Liahona Article - At Home with the Hinckleys
Church magazines: You have said that your father never laid a hand on any of his children when disciplining them. 4
President Hinckley: That’s right. I don’t believe that children need to be beaten, or anything of that kind. Children can be disciplined with love. They can be counseled—if parents would take the time to sit down quietly and talk with them. Tell them the consequences of misbehaving, of not doing things in the right way. The children would be better off, and I think everyone would be happier.
My father never touched us. He had a wisdom all his own of quietly talking with us. He turned us around when we were moving in the wrong direction, without beating us or taking a strap to us or any of that kind of business. I’ve never been a believer in the physical punishment of children. I don’t think it is necessary.
Church magazines: Sister Hinckley, you have said that “you don’t teach a child not to hit by hitting.” 5
Sister Hinckley: When my daughter Jane was a young girl, she said to me one day that she had a friend who was grounded. I said, “Grounded? What does that mean?” We let our children figure things out for themselves. They knew when they were doing wrong, and they would fix it themselves. One of our daughters decided to stay home from church one Sunday. So she stayed home. She got very lonely. Everybody was in church but her, and she just sat on the lawn. She didn’t try that again. She figured it wasn’t any fun. It was lonely.