Extra handler breaks Datepicker field
Looks like the problem is with the CSS rather than the id part. The typical id would be something like this: edit-field-date-und-0-value-datepicker-popup-0 and this id is dynamically generated and not grandee that it would stay same (i.e. you may get edit-field-date-und-0-value-datepicker-popup-1 if you have the same field twice in the same form).

You can use name instead of id. Here is the working fork of your jsfiddle with name: http://jsfiddle.net/vijaycs85/C4sh9/