My attempt was to find some way you could do this. However you will not be able to do it the way you suggest.
If the trust issues the check to a charitable organization, then the trust technically includes this on the form 1041 and changes the distributable income. (it is reduced).
I understand what you are trying to do.
Why not try this solution.
Since you all agreed to how the distributions to beneficiaries was to be handled, but minus the charitable contribution, you main concern seems to be that everyone fulfills their obligation.
Why not have the distribution to beneficiaries be made without regard to the charity, and to have the distributions go to an escrow account. The administrator of the escrow account can distribute the monies according to the agreement you have.
Under IRS ordering rules and accounting rules, the money is available legally to each of you when it goes to the escrow, because it is constructively received.
Then each person gets their distributions minus the amount that goes to a charity. The donation is made in their name. Think of it in the same way one might for a closing on a home.
in that way each person can take the charitable donations.