Hi Erin!
Thank you for visiting the Moms Panel!
A first trip to Walt Disney World is always a very exciting one, and you don't have very long to wait!
Epcot's Future World, opens at 9.00 am, and World Showcase opens at 11.00 am. I think you have enough time to visit Future World, and maybe some of World Showcase - or perhaps save World Showcase for another day so you will have time to see it all. There is more than enough to see at Future World, especially with your boys of ages 13 and six.
If you are staying on-property, and using Disney transportation I recommend allowing at least 60-90 minutes to travel from your hotel to your dinner reservation at
Disney's Contemporary Resort. If you are travelling from Epcot to
Chef Mickey's, I would allow 60 minutes in order to arrive in comfortable time. From Epcot you can use the monorail or bus.
If you have any other questions, please come back and ask me - I would be happy to help you plan your first magical vacation!