How to move an element into another element?

You may want to use the appendTo function (which adds to the end of the element):

$("#source").appendTo("#destination");

Alternatively you could use the prependTo function (which adds to the beginning of the element):

$("#source").prependTo("#destination");

Example:

$("#appendTo").click(function() {
  $("#moveMeIntoMain").appendTo($("#main"));
});
$("#prependTo").click(function() {
  $("#moveMeIntoMain").prependTo($("#main"));
});
#main {
  border: 2px solid blue;
  min-height: 100px;
}

.moveMeIntoMain {
  border: 1px solid red;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div id="main">main</div>
<div id="moveMeIntoMain" class="moveMeIntoMain">move me to main</div>

<button id="appendTo">appendTo main</button>
<button id="prependTo">prependTo main</button>

my solution:

MOVE:

jQuery("#NodesToMove").detach().appendTo('#DestinationContainerNode')

COPY:

jQuery("#NodesToMove").appendTo('#DestinationContainerNode')

Note the usage of .detach(). When copying, be careful that you are not duplicating IDs.