We were on the same 2 Cruises as Bats and can second the reccommendation for the tour company she used. Think there were about 5 or 6 minivans and everything went like clockwork.
The
DCL excursians are very expensive but you do have the peace of mind that the ship wont leave with out you. But for places From Ville France the train was very convinient and didnt involve us being off the boat for a huge amount of time.
We did have to tender For Ville France and I think one other port but think Naples and Roma were walk of the ship no tender.
I would suggest joining the cruise meet up post for your cruise and maybe hook your children up with some monitored emails from age approprate children also travelling on your cruise. It is a great way to ease them in to it especially as they have never cruised before as the kids clubs are great but can be a bit daunting at first.
Let the children order from room service is great fun but make sure you have some bills to tip room service with. They can order hot food and that inclued in the cost, but if they order bagged chips or candy or anything like that it will be added to your room bill. My girls loved ordering from room service it made them feel very grown up.
We love the Magic and it is the only ship we have been on so far. Wouldnt bother with the rain forest room pass as that area of the ship is a bit tired and dated. (ship is going in for a referb at the end of the med season, and it places it shows) but dont worry, it is just that she is in constant use but thousands of people with not much dry dock action in 14 years only every couple of years or so, although the last time she went in was 2010 I think as it was right after our 1st cruise.
As Bats says anything you want to know about the european cruise that we can help you with im another one you are better pming as I dont come over here as much as I used to.
Bring a small pirate costume for the kids for pirate night the costumes on board are excessive, and you can bring some bits with you even transatlantic and it shouldnt take up much room.

we did it this year on our new york cruise.
When you get on the ship make sure you have packed your bathers in your hand luggage so the kids can go in the pool straight away. Else you have to wait for your luggage to be brought to your room.