We have a good ten year span - not quite what yours is - but I know the challenges! We did a 4 night cruise on Royal Carribbean from Port Canaveral as our trial family cruise. It was extremely reasonable - $1200 for two rooms over President's week. It was another $400 on tips and a glass bottom boat excursion. We had 2 cabins - since we have 3 kids. Although it wasn't one of the newer boats, it had very good kid appropriate shows & kids programs. It also stopped at their island, which was a wonderful day. I'd really try to get on a boat that make a private island stop if at all possible, especially with kids. The teens went kayaking, we played in the sand with the girls and my middle child rode on the car track for about an hour, lol. It's really one of the best days of vacation ever. The food was great and the staff was wonderful - our youngest likes shrimp cocktail and the waiter would have some for her every night when we got there. I won't even go into the crazy big sundaes they made the kids. We are going to try a newer/fancier ship in a couple of years - but this was a good trial.
My suggestion would be get two rooms, and let your oldest bring a friend or two - the cost for the 3rd and 4th in a cabin is usually minor. Put the boys with you (just barely got a pack & play in the room - but it did fit) and make a deal with your oldest to be kind to the younger sister and also allow her and her friend time alone in exchange. Our teenager didn't really enjoy the teen program, because so many had siblings/friends along and he was kind of left out, so I think we'd have him bring a friend next time. Our middle child loved the kids programs and although our 3 year old was old enough, she just wasn't comfortable (hadn't been to preschool yet) - I don't think it was their problem, she was just a bit too young to be out of her normal element and not with us. That may not be an issue for you - we wanted to spend the day with the kids, but we did want to try and get dinner and dancing or a show with no kids, but it didn't really happen. We just ended up taking them with us, and it was fine - just not what we'd been hoping for.
Oh, we went to the Kennedy space center with this too - so it was two days of Kennedy space center, a day on the beach in St. Augustine and 5 days of cruise - really worked well. It ended up being about $2,500 for the week with tickets, hotels, etc etc. I'd try one of the shorter, less expensive cruises and see how it goes...hope it works out for you. We liked it - just learned we needed to wait til the youngest was a little older if we wanted time alone and bring a friend for a lone teen.