As the Gecko DOM Reference for Node.insertBefore() points out, this can easily be achieved with
parentDiv.insertBefore(nodeToInsert, nodeToInsertAfter.nextSibling);

If nodeToInsertAfter doesn’t have a next sibling, a NULL value will be returned and nodeToInsert will be inserted as the last child of parentDiv.

If you find it frustrating to type insertBefore when you want to insertAfter, that’s OK: you can add that function to the Object object:
Object.prototype.insertAfter = function (newNode) { this.parentNode.insertBefore(newNode, this.nextSibling); }

Now you can type:
nodeToInsertAfter.insertAfter(nodeToInsert)