We sailed Horizon last year April, sure not much has changed in a year so here goes.
Skyride is a must for you and your kids. Free activity and great views from the Skyride. Not sure height or age restrictions.
Because of the cost - I seriously would skip paying to do the IMax. You can always go to the movies at home. Watch a movie on the big screen on the Lido deck instead one night. Grab the free popcorn from the bar a few beach towels and settle the boys into a couple lounge chairs and enjoy. Usually at least 2 age appropriate moves for your boys each cruise.
We had no little ones with us but I would not miss the Dr. Suess waterworks area and some of the other Dr. Suess themed events. Depending on how mature your kids are this could be the last year they might these brightly color Suess area are cool. You might consider paying for the Dr. Suess breakfast - I have never done it and I have heard mixed reviews. Just search under Carnival on here and you are bound to learn more about the green eggs and ham breakfast. Shoots some hoops with the boys on the Sportdeck and a family game of minigolf is fun.
The kids may not like the Playlist Productions but we did as adults. This would be a great time to put them into the Camp Carnival and let them play with some other kids for a bit. Not sure your feelings on that. But my now 26 year old talks about the 2 cruises he went on while younger when he "met all the kids". I liked traveling and experiencing new things with my kid when he was young, so I did not use it as a babysitter all day. Just for a few times when I knew he would not enjoy what I was doing.
If you like BBQ, eat at Guy's Pig and Anchor during the day when it is free. But go there at night to listen to some good music. As a rule we usually do not go to any restaurants on ship where you have to pay, except the Steakhouse. We do not go to the Steakhouse each sailing but have on special occasions that coincided with the our cruise. Hint: Do the Steakhouse on the 1st night and I thought Cruise Elegant nights to receive the free bottle of wine. If I recall Horizon has the Italian restaurant that you can pay at night but during the day it is free. We usually hit the lunch Del Capitano at least once. No standing in line at a buffet, food delivered to my table. Just remember to grab your drink before going in to the restaurant. It reminds me of when Olive Garden does your "build your own pasta" special.
I am not sure if this is your first cruise or the first of your boys but a tradition I started with my son was to buy the nicer model ship from the gift shop and ask if the Captain can sign it. They look at you funny, maybe even object at first but I have never had it refused. I believe last time I had to take it to the Guest Services area. It was a great ship souvenir for him and used to display them in his room. At 26, who knows what he and his wife do, probably in a box somewhere, and assume he no longer buys the ships. But when the box is opened, he will remember his cruises with Mom. Ok, bit too nostalgic.
Most of this you probably already know but saw you were unanswered on your questions and thought I would help you out.