We have not done a Carnival cruise yet, but I assume they are comparable. If you want to drink something other than tea, water, normal coffee, machine juice then you need a drink package. We always have it because its free and we never had a problem ordering whatever we wanted. We aren't heavy drinkers and we aren't picky bout the quality of alcohol, if you are then you may want to upgrade to the premium.
And yes they nickel and dime you but so does every other cruise line. There is an upgrade for everything if you are willing to pay for it. But you don't need to in order to enjoy the cruise.
There are 3 main dining rooms that are solidly good. It's not the best food I have ever had but it's a solid good (and I am picky). We really like the Local, which is like pub type food, your twins would like it and it's also free. We like most of the specialty dining, it's not a must do but it is nice and they do have kid options on all the menus. You can also see the menus from each restaurant in one of the forums here. They are free so you might as well enjoy them. But again the dining room food is solidly good and the service everywhere is outstanding.
We don't have young kids, but I've been told the kids clubs are wonderful and full of fun activities. There is a lot of kid friendly activities and spaces on all their ships. They always look happy!
I would tell you to try NCL. You won't know until you do.
~Best of Luck
Terra