Gone through your scenario and code you shared :-
Can you please check with the below jQuery code as it worked for me. :-)
$(function(){
var vNewSelect = '<select name="new" id="idNew"><option value=""></option><option value="test1">Test1</option><option value="test2">Test2</option></select>';
$('#Resolution').change(function(){
if(($('#Resolution option:selected').val() == 'Internal Transfer') || ($('#Resolution option:selected').val() == 'External Transfer')){
$( vNewSelect ).insertAfter( "#Resolution" );
}else{
}
});
});
Hope you also will be helpful with the code shared.