Welcome aboard Ruth! I must say I am envious of the Disney vacation you have planned! 20 days full of Disney fun on the land and at sea! You are sure to have a very magical adventure!
I wish I had better news about parking your car, Ruth. Unfortunately, you are unable to leave your car parked at a Disney resort if you are not staying as an overnight guest.
Normally, I'd say that Disney's ground transportation is worth the extra $35 per person each way since they take care of all of the details. But since you wouldn't have a place to leave your car, you will most likely save money by simply driving yourself to the port and parking there, depending on how many people are in your party.
Check out
Disney Cruise Line's Port Canaveral parking information. You'll see that it will cost $170 per parking space for the 7-night cruise. Directions from the Walt Disney World resorts to the port are also listed here.
You might also check out Port Canaveral's Park n' Cruise (just do a google search online), as they offer close parking for about $5 per day if you make advanced reservations online. They also offer a shuttle from the parking area to Disney's cruise terminal. You might consider having one of you drop off the family with the luggage at the terminal while the other one goes to park the car, then meeting up at the terminal.
Either way, once you set foot on the ship, you're in for seven relaxing and event-filled nights, Ruth! Please let me know if I can help with anything else before you set sail!