I would like to help you with your question.
I think you are a wise and responsible parent. Absolutely...your son is trying to bully you and you are right in resisting. It's your cabin and you have the right to set rules about who uses, when, and so forth. If he does not want to respect your rules...then fine...he can't use the cabin. Period.
I'm sorry that your older son suicided. That is a very difficult grief experience and it is quite awful that this son tries to manipulate you by threatening suicide. He certainly knows how to push your buttons!
I'm glad you offered therapy to your son...that is a good approach to take to deal with his anger. If he refuses this help...well that certainly tells you something about how unwilling he is to take a look at his behavior. Here is where that tough love comes in!
Let me tell you my approach to suicidal threats. If someone threatens suicide I always...always...take is seriously. It is better to be proactive about such a threat then to run the risk of not doing anything. Understand? So...the next time your son threatens, put him in the car and take him to the nearest Emergency Room for evaluation. This will tell your son that you are unwilling to be manipulated and that you will take his behavior seriously. If he is truly suicidal...he will be get help...if he is trying to bluff you...well he will learn that their are real consequences for trying to trick you.
In my experience, the above strategy puts an end to idle threats as the child learns that mom/dad will act swiftly and immediately.
I'm sorry your son is acting immaturely and irresponsibly. I can only imagine how difficult this is for you. As you say, he is a good kid with strong potential in life...but his anger must be addressed. Stopping the suicidal threats may be one way to get him to realize that you care deeply about him and take your role as parent very seriously. This may be a "game changer" in how he treats you and what he expects from you. Still, however, is the issue of his anger.
If he knows that he can no longer manipulate you....that you will stand your ground on issues like the cabin...perhaps he will become tired of being angry and realize that therapy might be a good idea.
I await your response so that we can chat about this.