RE: Tough decision as a land owner.....
Since you heard about this from another source, discuss this with your parents and see how they feel about the situation. Depending on their response to your Uncles' actions, will help you decide how to handle the situation, but before reading them the riot act, call the uncle and inform him that you have been told they are taking slickheads (plural) off the property and since you had discussed with him that ONE could be taken off, you wanted to talk directly with him to see if the story is true. This will give him the chance to take the high road. If he admits it, listen to his reasoning and make an informed decision. As far as the cousin goes, he has totally disrespected you and your wishes. Explain to him in no uncertain terms that he is not welcome back on the farm.
Just remember whatever decision you make, it could be a decision you will have to live with the rest of your life.
I personally would not have a problem with them taking a few does for herd management, but I do not know how much property you have or how many deer you have roaming about.