Have a look at the code posted in this thread:
basically, the idea is that when the first date is selected the minDate for the second date is set via options.
No need for validation or blocking the form submission - the user just can't pick a date that doesn't make sense.
For extra security, you can make those inputs read-only. The date picker will still work on them, but you won't be able to type values in from the keyboard
oh, yes - and as Andrew points out, the datepicker will only work using the IDs of the inputs - class names are very problematic