Hey Faith!
It's easy to obsess about our Disney details!
But your transportation shouldn't be a big hassle, I wouldn't change the dinner.
Here are some options:
Your family could take the boat or Monorail over to the Magic Kingdom and from there hop on a bus to the Beach Club Resort where Cape May Café is located.
Or, you could take a bus from your Resort to Disney's Hollywood Studios. From there you take the boat over to the Beach Club Resort, or walk along a nice path. I really like that boat ride...relaxing with a lovely breeze.
With those options above you don't actually go into the Parks...you are just transportation hopping!
Or, if you are impatient like my family.... we ask the Concierge to call a Taxi for the family. It usually takes less than ten minutes to get anywhere on Disney property and rarely costs more than $15.
I hope that your family has a wonderful time in September!!