Getting driven to Clearwater (I presume for an entire day?) is a seriously expensive proposition, and that is why there is so little demand for it. The reason in most cases is that once that car goes to Clearwater in the morning, it will either have to stay there all day or drive back to Orlando empty, then go back to Clearwater empty before your fare back. You have to pay for all 4 legs to make it worth their while.
There is a "beach and lunch" excursion bus that is run by AllOrlandoTours, but it is $100/pp. It includes the r/t bus, a picnic lunch, and a ticket to the Capt. Memo boat tour. That is seriously steep pricing for a family.
Honestly, this is one time where the hassle of renting a car is FAR outweighed by the inconvenience and expense of NOT renting a car. Clearwater is a fairly straight 90 minute shot from WDW; interstate 85% of the way. You just head for the Tampa airport via I-4, pass it, and keep going straight across the causeway to the barrier island, and then drive straight on until you see nothing but beach in front of you. Also, having a car means you can take a side trip to the Clearwater Marine Aquarium if you want; it's a great stop for kids. (It is a rescue facility, not a typical aquarium.)
You can rent the car on WDW property the evening before, park it at your resort and head straight out first thing in the morning so that you can be at the beach early. Take a little collapsible ice chest and hit a Publix in Clearwater to pick up your lunch at the deli.
(A one-day rental runs for 24 hours.)