Hi Jann! Disney offers
Complimentary Resort Transportation throughout Walt Disney World for its guests. You can take buses, boats, and monorails from the resorts to the parks and Disney Springs.
When guests ask about the fastest transportation it is not always the complimentary options but instead it is calling for a taxi. It is easy to call or have your resort call for a Disney Yellow Cab (407-422-2222) when you are needing to go from resort to resort. It does cost extra when you are on a vacation budget but many times it is worthwhile as it alleviates extra stress for the family.
You will actually have two choices to get to your Cape May reservation at the Beach Club Resort. You can take the Epcot bus from the All Star Movies resort and then walk to the International Gateway exit to get to the Beach Club. The walk could take around 30 minutes so please plan your timing accordingly. I would try to leave your resort around 9:30/9:45 so you won't have to rush and hurry and stress. Although the World Showcase does not open until 11am you will be allowed to walk past Canada and the United Kingdom to exit out the International Gateway.
Your second choice would save time and that is to call for a taxi to take you directly from the main building at the All Star Movies Resort to the front door of the Beach Club Resort. This trip will take only about 20 minutes so it allows you to sleep later or even get a morning swim in for the kids before you go to Cape May. The taxi cost would be about $20 and if you need car seats request that when you call. They have larger van taxis if you have a large family.
Hope this helps and it gives you options.