This is a quick script on how to can compare 2 dates and ensures that one is larger than the other. Please put this script in a Custom HTML element in your form. Remember to enclose this coding in the <script type="text/javascript"> block.
$('form').submit(function(){
startDate = $("input[name='start_date']").val();
endDate = $("input[name='end_date']").val();
if( endDate < startDate ){
alert("End Date must be larger than the Start Date. Please try again.");
return false;
}else{
return true;
}
});