How do we help my brother overcome his grief?
Many grieving individuals turn to substances such as alcohol or prescription painkillers to dull their emotional pain. Unfortunately, this "medicine" can become a bigger problem than the grief itself.
As for what steps the family could take to help Brother 2 get on with his life, there isn't that much that you can do unless you have his willingness to hear and heed your counsel.
Should Brother 2's drinking become problematic, the family has the option of arranging family counseling sessions to address the issue and its impact on the family. Or if his drinking is really serious, a family intervention may be necessary. Alcoholics Anonymous is an excellent program available in virtually every community. Besides the number of people who've used this route to address their drinking, another selling point for this approach is that it is free.
Since it has only been a short time since Brother 1's death, it isn't surprising that Brother 2 would be having difficulty shifting gears to engage in career exploration. It seems important to honor his clarity about not wanting to do nursing while at the same time, helping him see the necessity of finding a new life purpose.
Just know that many folks in the grieving process go through a real period of floundering, and it can last much longer than a few months. My bias, however, is that the duration of this could be drastically shortened by grief counseling.
I was the caregiver for my wife for six years of a battle with cancer; I cannot even begin to imagine what Brother 2 went through, because being the caregiver damn near sent me to a nervous breakdown.
The only thing I can really offer is this: after she died, I was very lost for a while, because I felt like I had no purpose in life. It took me a very long time to realize that I had completely reoriented my life around caring for her, to the point where it was now ingrained behavior for me. When she died, all those new patterns and behaviors I created for myself were suddenly cut off, leaving me to feel lost and without purpose. I tried a lot of different things, from volunteering, to old activities pre-cancer, but nothing felt right.
As dumb as this sounds, it wasn't until I got a puppy, this sickly runt who was an odds-on favorite to die before six months, and threw myself into taking care of her, that I started to feel human again. Thankfully for me, she survived and flourished (I shudder to think what might have happened to me if she hadn't); in a strange sort of way, the puppy was my redemption. I know, mentally, that there was nothing I could do to cure my wife of terminal cancer, but there is some part of me, as her caregiver, who despite doing a pretty good job for a non-professional, felt like a failure for "letting her die." By nursing the puppy back to health, it was like I had redeemed that part of myself that would not let go of the guilt.
Like I said, it's a dumb story, and I don't know if it in any way can apply to what Brother 2 is going through, but grief is a strange mechanism.