Welcome to Cruisemates,and congratulations on your upcoming engagement.
I think of the 3 ships you mentioned, I would select Liberty....I was on her sister ship, the Freedom,and really enjoyed the layout of the ship, and all they offer..RCI will have the smallest cabin of these, if that makes a difference. They also have a rock wall flow rider, centrum parades and a main deck shopping and dining avenue..Fun atmosphere, for sure.
Now Carnival will give you the largest cabin, and may have more kids. I think all your choices, have good food, though RCI within the past few years has gone down, according the general consensus. I do know someone off the Connie, recently and they enjoyed the food and service.
When are you planning to do this? Time of year will make a difference as far as kids onboard. Let us know more of your interests, aside from this special reason.