We did our 1st. European cruise last September and know exactly what you are going through. Even though it may be warm, you want to be dressed respectibly. I suggest cotton outfits; capri pants, jumper with a T, sheath style cotton dress (the teens will look great), a casual resort style outfit that would have a little jacket to match, etc. No mini-skirts, abreviated tops or tank tops. Closed toe shoes for the Vatican are recommended or when doing a lot of walking; aerosoles four-way or fisherman style shoes are great. Just make sure to be comfortable, too. Take a back pack for a water bottle, to put your jacket, camera, souvenirs etc. into.
Bon Voyage