Although drag-and-drop reassignment of child pages to new parents would most simply be an integral part of the standard Pages tab, this could become troublesome if the overall hierarchy is wide and deep and a page needs to be dragged a distance that scrolls off the screen.

An easier implementation might be two steps. On the Pages tab, clicking a "relocate page" link on the child row. Then clicking a "new parent" link on the target parent row. The "new parent" links would dynamically appear after clicking "relocate page" and the "relocate page" link would disappear. Would probably need a "cancel" action to abort a reassignment in progress. Next to the "cancel" link would appear "Relocating MyPage?" naming the title of the page being relocated.