Assuming both the parent window and iframe content are on the same domain, you can try using the window.parent
as a context selector. Try this:
var moveFrom = $("#image1", window.parent.document);
var moveTo = $("#image_group_2", window.parent.document);
moveFrom.appendTo(moveTo);
If the domains are different, then you will not be able to achieve this, using either jQuery or native JS.