DRS, if you don't mind me saying so, I think a compromise may be in order. It would be a shame for you to miss the dining room, and I also understand his desire to wear jeans. Perhaps he can wear the dockers and golf shirt a couple of nights (so you can experience the dining room), and then have dinners the remaining nights in a more casual setting.
While I haven't seen Norwegian Pearl yet, I have visited sister ship Norwegian Jewel and the main dining room was stunning -- among the most beautiful I've seen (and I've been on a lot of ships). Still, khakis or dockers with a collared shirt are fine for the dining room.