I traveled on the Spirit last July with my 17-year-old son and my parents. Originally we were booked on the Sun but it hit an iceberg and canceled our cruise so we moved our dates to the Spirit instead, kind of quickly. I missed that there was nothing for under 18 there until it was too late.
There weren't very many kids on the boat that I noticed. My son wasn't all that upset that there was no teen club as he's kind of shy anyway. He had no issue in restaurants, Bingo, etc. (you have to buy the cards for under 18 and play with them). Can't go into the Casino and I remember seeing on the Daily thing that some comedy shows I think they were for 18+ only. We didn't do any of the main shows so no clue there. No movies. We'd go for some drinks in the Spinnaker after dinner. He never really wanted to join us there so I don't know if they would've kicked him out or not. I do remember seeing some kids on the dance floor there a few times.
I will admit my son got pretty bored and I felt bad for him as there wasn't much for him to do. He did sit in the hot tub some on the main deck, not the adult area and nobody bothered him about that. Too cold to swim for his taste. The biggest thing that upset him was the sports deck was open for very limited hours and was always closed by 5. He wanted to play BB and stuff as that was about all there was to do but it was often closed. He loved Alaska though, so I don't think he'd tell you he had a bad time, but I know he did feel like there was just nothing for him to do at all. I am glad I got the unlimited wifi for him so he could watch Netflix movies or whatever in the evenings. If I were to book it for Alaska I would choose a different ship. The good thing for you is your kids have each other and that might help them entertain each other where my son only had me and his 70-aged grandparents.