Hi Elaina,
I completely understand not wanting to take a laptop on vacation but you still want to chat with your husband.
One option is to go to a business center which will have computers. However, while these will work for emails or searching the web, I am not sure if they are equipped with webcam capabilities. The following resorts have business centers: Boardwalk Inn/Villas, Contemporary, Coronado Springs, Grand Floridian and Yacht Club.
Another option might be an app on your smartphone, tablet or iTouch. Using Skype or another app you might be able to chat with your husband. Most lobbies of the convention centers will pick up wireless.
Finally, you can send internet postcards from a few locations in Epcot so dad can at least see you until we return home.
Wishing you a magical vacation!
Beth