I made a donation to a tzedakah institution and this institution publicly embarrassed a close friend of mine by firing him in a very public way. Am I allowed to ask them to return my donation or to give to another tzedakah?
You sound very upset, that the institution fired your friend, and you want to stick up for his honor. Once you made the donation, the money belongs to the institution, and you don’t have the right to ask for it back, or to demand that they give the money to another institution.
Right now you are mad at the institution because you close to your friend and you heard his side of the story. It is possible that if you would know the other side, not that you would agree with them, but you wouldn’t be as angry with them. (I don’t mean to say that you should get involved and try to find out the other side of the story, rather that things aren’t always as extreme as they seem, once one sees the whole picture. Therefore even without knowing the whole picture, it is possible to dan l’kaf zechus.) Besides, for your own sake, although you should sympathize with your friend and help him out in his time of distress, however we are not allowed to join in the fight. (This is the lav of “Lo t’hiye k’korach v’adaso.) Therefore for your own sake, give your friend the support that he needs, but don’t jump into the pit that korach is in and join the fight.
Hashem should bring peace and bracha to all of Klal Yisroel.