I've no idea about the drinks as I've not been on Costa. If you dock where we've usually docked I believe it is possible to walk to the main sites but maybe not with six young children!
You can get a water bus a short walk from where you dock that will take you right to the centre for a few euros return, the kids will enjoy that I imagine :-).
Re Drinks package,
Costa sell a bargain X1 package for adults about £7 a day, includes unlimited water beer wine and soft drinks with all meals. Even though not for kids the waiters will bring as many cans of drinks that your kids could possible drink. The only drinks package as such for the kids is a booklet of vouchers which makes the fizzy drinks slightly cheaper and the non alcoholic cocktails quite a lot less. Just get them to fill up at mealtime!