Hi Ryan,
You are my kid of family. I LOVE Pirates of the Caribbean and was so excited to get to see the new pirate rooms at Caribbean Beach Resort. They have some great fun details that have been added from the boat beds to the "wooden" carpeting and pirate curtain. Unfortunately there is not a daybed in these rooms and there is no cots available at any Disney resort. Another moderate level choice that would offer space for five is Disney's Port Orleans Riverside Resort. This resort has a limited number of rooms that feature trundle beds to accomodate families of five.
A great option for a family of five, near Magic Kingdom, is the Polynesian Resort. This resort has very spacious rooms that feature two queen beds and a daybed. This resort is located on the monorail with easy access to Magic Kingdom, the Ticket and Transportation Center and on to Epcot.
You may also want to consider the Fort Wilderness Cabins which can sleep up to six. The cabins have a bed and a set of bunk beds in the bedroom and a pullout couch in the sitting room. This location is a Magic Kingdom resort, however it is not located on the monorail and would require the use of buses or boats to move from the resort to the parks.
You could also look into the availability of a villa at the numerous Disney Vacation Club properties. These villas offer a number of different sizes and would give your family plenty of room during their stay. You can visit
here for additional information on these properties. Regardless of which property you pick, I am sure your family will have a great time as they are all wonderful choices!