Change parent of multiple child pages
I'm assuming your parent-child relationships are done through an Entity reference field on the child node pointing to a parent.
As always there is more than one way of solving it in Drupal but one popular way is to use the Views Bulk Operations (VBO) module.
The module Views Bulk Edit helps to speed it up by showing the field options to update.
The procedure is to create Views where you can see all the child nodes among the results. It can be all nodes of that type, or you can even create it specifically for one parent node where its children nodes are automatically filtered.
VBO allows you to add a Field to your Views that shows up as a checkbox next to each result row. It also adds an Action you can trigger on the chosen rows.
With that configured you will be able to choose nodes from your results and edit them in bulk.