Seven days at Universal would be way too long in my opinion. There's only two parks. If you do the Universal/cruise package everything will be included. It will include hotel/admission tickets/transfers from airport to Universal to the pier and back to the airport.
If you decide to do Disney World I would stay at an onsite Disney property. It will be a better experience. If budget is an issue the Disney All Star Movie/Music/Sports are very economical. When staying at a Disney property you will have access to early park entrance/late stay at park, for the designated park of the day. You will be able to purchase gifts in the shops and have them delivered to your hotel (no having to carry them around). When staying at a Disney hotel you can add on a Disney Meal plan. There are several different plans. The Quick meal plan provides plenty to eat in a day for most people. In the past Disney meal plans were pricey but now they are a pretty good deal. Also Disney shuttles to/from hotel run more frequent then off site hotels. Disney provides the Magical Express transfer from the airport to a Disney hotel free of charge and back to the airport. If you are doing a Disney World/ Disney cruise package then all your transfers to the pier and back would also be included. If you did Disney World but a Royal Caribbean cruise, you could have a transfer company pick you up at a Disney hotel and transfer to the pier without going clear back to the airport. Also, if you did want to rent a car to go to the pier there is a car rental at the Dolphin hotel and Disney Car Center over by Downtown Disney.
I've been on three Disney cruises and have enjoyed each one. My first Disney cruise had about 600 children but you never would have known. Disney has excellent programs for the kids. Disney doesn't have casinos and the space where a casino would be, is turned into a hands on interactive area for the kids. There are plenty of adult only areas on a Disney ship.