Hi Paula! The good news is there are advantages to all the deluxe resorts so you will have an awesome vacation no matter which one your choose! The first one that pops into my head when you mention you want to relax is the
Polynesian Resort. The grounds are absolutely beautiful and the kids would absolutely love the volcano pool - the slide is actually inside the volcano. You have access to boat rentals at the marina which is always a fun time. This resort is located on the monorail so there is easy access to Magic Kingdom. You can also walk to the Transportation and Ticket center which would make it super easy to get to Epcot.
If you want something a little more upbeat, you may want to look into the
Beach Club. The big advantage to this resort is it shares a mini water park with the Yacht Club. You can relax on the lazy river while the kids enjoy the pool slide. Additionally, it is located on the
Boardwalk which is a destination in itself! You can visit the Boardwalk Bakery, ESPN Club, rent a surrey bike, enjoy the street performers, etc. As far as transportation, you can easily walk to Epcot but there are also boats available to Epcot and Hollywood Studios.
If you don't think either of these options will work for you, please write back for more ideas. Have a wonderful vacation!