You are focussing too much on what they say they will or will not do. Complaining and expecting them to help is not happening.
You can point out to the admin of the group that as he has been notified of the defamatory material, as of xxx date, and elected not to remove it, he personally can now be sued for defamation as a publisher.
I can't say what effect this is having on your charity, but you are now left with the choice of dropping the matter, or if you are serious about wanting to protect your charity, sending them both a cease and desist letter and a demand for removal else they will face legal action. You have rights, but seem reluctant in wanting to enforce them.
BTW, I am not saying or even suggesting the material is defamatory. I have based my opinion solely on yours.
An observation here: Charity people are often too nice for their own good. Sometimes you need to take a stand and do what is best for your charity even though it means you have to be confrontational. It can be hard because that is not in the nature of many people wanting to help others, but if you want what is best for your charity, take a step outside your comfort zone, and stand up for your rights.