M.P.
I sympathize with you and your family. I'm a retired police officer who has dealt with suicide. I've also been a Crisis Intervention volunteer with the added experience of dealing more closely with the family.
Your wish to write a letter is what you should do. Say just what you said here; that you love and support him. I don't know about the service and how long it will be before he comes home. So, send it now. Don't wait until he gets home.
You should write whatever your heart tells you to write. Make your words positive and supportive. Don't ask why or specific questions about what he did? Don't be critical of his choices that led him to this place.
I just realized that I do have some experience with this and the service. Quite a few years ago my cousin had an emotional breakdown when he was in the Air Force. He didn't attempt suicide. He threatened it and was found drunk on someone's lawn. He was hospitalized, diagnosed with schizophrenia, and then given a general discharge. He had been in ROTC in college and this was his first assignment after graduation.
Both he and his family felt that the Air Force treated him well. They provided for psychiatric care until he was able to be discharged from the hospital and could go home.
I can understand both protocol and the feelings that you and your family must have for the 3 day delay. His parents should have a phone number for a contact person and could ask for an explanation of the protocol and reasons for it. At some point, someone should be able to explain this to them. Now may not be the right time for this question, however.
Now, the concern is what is going to happen from now on. If the contact person hasn't told them or if they don't understand then they should call and ask and they should insist on an answer as regards to service protocol. It could be that they (service) don't know because they are waiting for the medical people to make decisions. It could be that your nephew has not given the service representative permission to give information to his parents.
This is one of those situations that requires patience and one step at a time. You do have to wait until the service sends him home. The decision is made by the service. Until he's discharged the service is responsible for your nephew. They will make recommendations for your nephew's next step but once he's discharged they cannot enforce any action. Because he's an adult, his parents may not know what those recommendations are. They'll have to depend on what their son tells them.
Once he's home be as much yourself as possible. Let him know that you're there if he wants to talk. Don't quiz him. Just show that you care and want to help in any way he needs. Don't be surprised if he's withdrawn and doesn't want to talk. Or he might want to talk and talk. He's the same man he was before he left but with this one very difficult experience. He'll probably feel ashamed. He may think that he's "no good." He may be sorry he was saved. He may be thankful he was saved.
Express concern but don't over do it. Expect him to act like an adult; an adult in pain but still an adult, capable of making his own decisions without your help. If he asks for advice give it. Be sensitive to his feelings but don't work at protecting him from them. He has to accept and express his feelings before he can heal. He will most likely need therapy to do this.
When I've been with survivors of suicide and with their families, I've found the most helpful thing for me to do is be myself, accept them and whatever they say or do that is not harmful to themselves or anyone else. I've shared tears a couple of times. Within my own family, I've found sharing tears the most helpful way to be close and deal with the pain.
I don't have any reading recommendations. There must be Internet sites that would point you in a helpful direction. I imagine that there are sites that in themselves will give you answers.
You are in the midst of a challenging and painful situation. My thoughts are with you. I want to encourage you by saying that with love and compassion there isn't anything that you do that is wrong. You'll be able to figure out what to do as you go along. My thoughts and prayers go out to you.