@Lmhodge,
Whenever I hired someone and they had a close -in conflict due to some long planned vacation or education opportunity (like within the first year of their employment when they were only earning their vacation time), they always brought this to my attention during their job interviews and seminars and I was generally favorably inclined to grant the LWoP. However, we dont have that opportunity here with you .
Going with the truth is a big first step. The only hole that I see you in is the fact that you only are bringing this up NOW with less than a month till June. YOUR TIMING IS NOT THE GREATEST.
Are jobs in your field easy to come by?
Do you want to retain this one?
I think you should weigh these options when you consider taking this family vacation.
Ive got no answers except as an asshole boss who will first look at you and say
"Hey, why not wait till Memorial Day to break this one to me?"
Sorry for being blunt but you may need to give it your best shot ON YER OWN and then still be prepared for a NO. And if you arent granted the LWoP, dont hold a grudge against your own boss she has a program or business to run smoothly, thats how she gets to take a vacation every so often.
Now, youve seemed to indicate that your "Site coordinator" (What does that mean?) seems to be on board. Is your site coordinator the next level up? Can you use that persons tacit agreement to carry forward to your big boss? Are you sure that your site coordinator didnt already say something to the Director? (that would be less than ideal wouldnt it?)