The initial setup should be as follows to be able to access both fields during your code validation.
Code Validation: Enable
Ajax Validation: Enable
Additional Fields: DATE_FIELD_1
The above would be configured on DATE_FIELD_2. The additional fields is crucial as without that you won't get the current value of DATE_FIELD_1 and will only get the already stored value. Now your code can simply substitute the values of both fields using [DATE_FIELD_1] and [DATE_FIELD_2]. Please be sure to always treat substitutions as strings so surround them in quotes as needed.
Since this is a simple is X greater than or equal to Y check you can just use a strtotime to check this. Example as follows.
Code:
return strtotime( '[DATE_FIELD_2]' ) >= strtotime( '[DATE_FIELD_1]' );