There's always a reason for not taking a vacation but there is absolutely no excuse for not leaving those reasons behind for a week or better yet, two weeks.
In my 35+ years in this industry I have never heard of an organization failing so badly in two weeks with the executive on vacation that they had to close the doors. It's like saying (God forbid) if you die the organization will have to close because they can't live without you.
Go away. It's unfair to you, your family and the organization if you don't.
As for the work, you will do more and get more done in those first two days when you return than you would have done in the entire vacation week that you skipped.
Did I mention go away? Your team and volunteers will figure it out until you get back.