Basically, you want to loop through each direct descendent of the old-parent node, and move it to the new parent. Any children of a direct descendent will get moved with it.
var newParent = document.getElementById('new-parent');
var oldParent = document.getElementById('old-parent');
while (oldParent.childNodes.length > 0) {
newParent.appendChild(oldParent.childNodes[0]);
}