Sorry but the dress code answers I have are a generalisation. Princess are amongst the more dressy-up ships. Does the website/brochure pictures not show people in them? what do they dress like? Use the 'contact us' button on the cruise company's website. I would think that the only time you will dress formal is on the probable 4 formal nights in the main dining room.(This sounds like a back-to-back cruise & there will be, on each week, a sailaway & captain's farewell formal nights). The small print should say that you can be booted off the cruise if you attempt to 'smuggle' drink on board. Do you believe them? It's up to you. Some people we've come across have put them in the suitcases before leaving the UK, & got away with it! Even leaving 'the evidence' in the room's fridge, without the cabin boy blowing the gaff. Consider not booking any of the ship's port excursions, the Caribbean is very 'user-friendly' in just walking off. Don't get immeadiatly drawn into the hassle, it can be very intimidating for cruise virgins. We in the past - on a first time for an island visit - have just said "No thanks, we have been here many times before, we are just having a wander around" Earwig other passengers, listen to what's on offer, suggest joing up with them if you fancy what they are doing. Don't pay anything until you get back to the port. Make sure you are back 1 hr before sailing, which is half an hour before the 'latest time back on board' (Does this make sense, the half an hour before sailing is the 'last passenger on board time', so back half an hour before that).
In my experience Princess cater for all dress codes - americans are not normally dressy people. Dress code in the restaurants in the evening is smart trousers and an open neck shirt. The Sterling Steakhouse operates the same dress code. The only nights you really need to dress up is on the formal evenings when either a suit or black tie is optional. If you want to stay casual you can eat in the 24 hour restaurant any time of day. Yes, wine is relatively expensive but you can buy a bottle, have a glass each and ask the wine waiter to save the remainder for the next time you are in. No hassle at all. There are also fast food eateries for the kids so I really would not get too worried about the dress code issue but we always find that on those rare nights its a bit of fun to see everyone dressed up - I am sure a shirt and tie is fine for the boys. We think Princess ships are great, so look forward to a great holiday!