Hi Kimberly,
It's nice to receive a question from a fellow citizen of Maryland. Thank you for sending this in!
If your parents need a refrigerator and a stove, then I recommend that they stay in a cabin at Fort Wilderness or in a 1 bedroom
Disney Deluxe Villa. Deluxe Villas are basically Disney Vacation Club (DVC) properties but you don't have to be a DVC member to stay in them; they are spectacular though expensive places to stay. Both will have what they need. A cabin at Fort Wilderness will be less expensive, but its location may make it problematic for your family. Due to the size of that resort, there is an internal bus system to move guests around, though some guests rent a golf cart to be used at Fort Wilderness at their leisure.
The closest Disney Deluxe Villa to the Caribbean Beach Resort is the Boardwalk Villas. However, you can't walk between the two resorts so I don't think it really matters how close they are to you. That said, I love the Boardwalk Villas and the Beach Club Villas. Both are on Crescent Lake between Epcot and Disney's Hollywood Studios. Your parents could walk from the Boardwalk or Beach Club to the International Gateway entrance of Epcot. They could also take a boat to either Epcot or the Studios. The Boardwalk area at night is very nice with restaurants, shopping, and night clubs.
If you both wanted to stay at the same resort, then I recommend considering either the Wilderness Lodge or the Animal Kingdom Lodge. Both of those are Deluxe resorts but are slightly less expensive than the other Deluxe resorts. They both have DVC properties attached to them, which would give your parents what they need.
Good luck and have a magical vacation!