Is the zip line worth it....hmmm... tough questions. I did it in Jan. It is $85. My reaction was ABSOLUTELY! I am 60 and my wife is 59. She is afraid of heights. It was worth it just to get her to do it :) It is pricey to say the least. We were on Freedom for the New Years cruise and the ship was full. We did not book the zip line but when we left the ship we simply walked over and asked if there was room and there was (there were 4 of us). We all enjoyed it. It takes awhile as you start with a short "training" class, followed by a small zip line to learn the "positions." Going down the big one you are assigned a line and position depending on weight and winds. We had a wind (not really noticeable) but some of the lighter people needed to pick up speed (torpedo position) or they wouldn't reach the landing platform. I am heavy so I needed the "starfish" to keep from building too much speed. Anyway, we were on Allure in Sept. and didn't do the zip line so decided it is sort of a once in a lifetime event so...heck... why not. Had a great time and I was able to tell my grandkids about it. Only other fees at Labadee are for various shore tours, or the water park area. I think it is pretty cheap, but it may be more juvenile than your kids will want. The best beach is Columbus Cove. As you head down the dock you'll see a ferry that'll take you there. You can also walk. It is the original Labadee beach and very nice. It is also where the water park area is. There is also a large straw market. Typical stuff. You use your cruise card and soda card for drinks, and lunch is free. RCCL has done a great job with Labadee.
As for ice cream, I think all RCCL ships have a soft serve dispenser somewhere near the pool. As for keeping the kids busy, I have never cruised with kids (mine were in college for our first cruise), but I believe there is a good teen program aboard. But the ship is beautiful and truly out classes anything Carnival has (except no slide). I suspect your kids will find plenty to do. Have a great time.