I think you have to have an organization with 501c(3) nonprofit status for money raised toward a cause to be nontaxable. We looked into it for a booster club.
The idea of donating the cash via rental instead is a good one as this would also give you a tax deduction for yourself.
Regardless of the recipient's nonprofit status, as stated above, the donation of the DVC vacation will not be tax deductible for you. The IRS will only allow it if you are donating your entire DVC membership (yikes!).
Very nice of you, btw, to think of others like this and helping out charitable causes.