If the designated supervisor (assuming it's not the other parent) is a third-party, you may be able to agree on a reasonable substitute during that person's vacation, or try getting an agreement (preferably written for future purposes if necessary) to allow unsupervised visitation for the same period. Otherwise, you may have to find another way to engage in visitation (e.g., phone, email, Skype or similar webcam talking, instant messaging) during the interim.
I agree with Daniel, you may want to get this modified to avoid any of this madness in the future. I wish you luck!
This response does not establish an Attorney-Client relationship. It is highly advised that if you wish to discuss this further that you inquire into hiring local counsel.
It's not clear from your post whether this vacation is a one-time event. If it is, you may consider whether it's just not worth it to fight this. If this is a recurring event, then you have more reason to seek some modification.
Sign up to receive a 5-part series of useful information and advice about child custody law.