You're dealing with what most of us deal with when joining the armed forces
How true! I joined in 1983, and while I was in the decision process, my mom was dead set against it. I had moved from LA to North Carolina to work construction at Shearon Harris, and after a year of that, started looking at other options. The Nuclear Navy sounded pretty good, and I told mom about it.. She was so distraught, that she said "Bill, come home and go to college. You can live here, and I'll pay your way through 4 years of school." The wisdom of me turning her down is another topic, but luckily, we had an old friend of the family that was in the Navy reserves. He had his opinions of the "Nukey Navy". Pretty much told my mom that they were the best and brightest, academic elite, and all of us walked out after 6 years to champaign dreams and caviar wishes! Those words, from someone she trusted, was all she needed. The next thing you knew, I had made a "good decision", for a "successful future".
So, if you know anyone in the navy, or military even, or your former countries navy, who your parents trust, and knows the remotest thing about nuclear power program (in a good way), maybe that would help get behind your decision.
One other idea.. I don't know if your parents are big readers, but the book "Hunt for Red October" paints American nukes in very positive light. Maybe you could have your dad read it.
Best of luck,
Bill