In an earlier episode ("The Camping Trip" - Season 2, Episode 29) Ethel already knew how to drive, and drove to Lucy's campsite several times.
During the final scene, Lucy pauses for a close-up shot and a large fly lands on top of her head.
There is some kind of fabric on the ground in front of the car when they all go out to see the new car (possibly to cover up the cable they use to pull the car?) When Ricky lifts the hood to see the engine of the new car and Lucy honks the horn startling him he jerks around and you can see where he causes it to fold just slightly.
When Lucy starts to drive the old Cadillac with the Pontiac in tow to the garage, you can see there is actually a cable near the ground pulling the cars forward. The cable gets taut just before the cars start to move.