Your job will be to qualify on various watchstations.
While standing watch, your job will be to operate the equipment on that watchstation that keeps the plant running, providing propulsion and electrical power to the entire ship, so the ship can fulfill it's mission.
Your job will be to attend continuing training, 2 hours per man per week (at least it was when I retired in 2011).
Your job will be to maintain some semblance of physical fitness so that you can successfully pass your twice-a-year PRT.
Your job will be to maintain your physical appearance to the Navy's grooming standards, i.e. shave, haircut in regs, uniforms clean and unwrinkled, etc.
Your job as a Nuke is not so different than that of any other sailor, because that's what you are; a sailor.
Everyone in the Navy works to fulfill the mission; whether that's drug interdiction around South America, power projection in the Pacific, or providing air support for ground troops in some part of the Middle East.
Sailors do all of this while confined to a ship or sub, miles away from your traditional family. The challenge that every Nuke faces, whether they will admit to it or not, is whether they are going to do what they are told and not b1tch and complain about it or whether they are going to be the "squeaky wheel". The vast majority of the squeaky wheels I encountered weren't squeaky to get things fixed; they made the noise because they were borderline sloths who wanted to get all the reward without the requisite work.
Life as a Nuke will be first on, last off. This means you are the first people on the ship, because it takes some finite amount of time to get the plant started up so the CO can get underway at the prescribed time or early. It also means that when you get back pierside, the rest of the crew is commencing liberty call while you are shutting down the plant.
Being a Nuke, to me, meant doing all of this, for around $8.00 a day more (your Nuke pay per month) than your non-Nuke peers because someone has to do it. I enjoyed being a Nuke; I despised some of my shipmates because comparatively speaking, we did about 5 times more in any given day than they did. But, I accepted it because of the skill set the Navy was teaching me. That skill set can be an excellent stepping off point for you when you transition back to the civilian world.
Hopefully all of this winding text has helped provide a little better understanding of what life is like as a Nuke. your success and failure will be in your hands. Put in the effort, reap the rewards. Expect NOTHING to be handed to you, especially because you are a Nuke.
Best of luck and thank you to both you and your brother for volunteering to serve!