If a child is holding a muktzah item on Shabbos and is hankering to be picked up, the halachah is determined by the value of the item. For example, if a child is holding an even, a stone, which has no value, we are permitted to pick up the child while they are holding the muktzah object and we are deemed to be moving the muktzah only indirectly. Since this was not done to protect the muktzah item, it is permissible. Halachah permits the parent, or other adult, to carry the mukztah in an indirect way through the child because the child will be distressed if not picked up or if we force them to drop the muktzah object. However, if the child is holding a valuable item, even if the child will be upset if not picked up, we may not do so, nor are we even permitted to hold the child’s hand while they are walking. This is because we are concerned that the child will drop the valuable muktzah item, and due to its value, the adult might pick it up and thereby move it, violating the prohibition of muktzah. Likewise, if we are concerned that the child will damage the item by holding it, or lose it, we may not shake the child’s hand to make them drop the muktzah object. This is considered moving muktzah indirectly, for the sake of protecting the muktzah item, which is forbidden.