Now, to your questions. You do not need towels. They provide them for the pool area and even to take ashore in ports, although they charge a lot if you lose one.
Jeans, even jean shorts, are too hot for most people in the Caribbean. Around the pool and on deck, you'll see people in shorts and tanks or bathing suits. But, not in the dining room, especially not for dinner. In fact, you may not even be allowed in the dining room for dinner in anything that casual. Depends on cruise line and the maitre'd. Try very hard to talk your dad and his friend into bringing dressier clothes for formal nights. I don't agree with some people who are very rigid about dress codes, but I do agree that you need to dress up quite a bit more than you would at home.
But, focus on your wedding and honeymoon. Nice that family will be on the same cruise, but don't worry too much about them. A honeymoon cruise is very special!