You would need two motors, and two speed controllers.
The RC Receiver would be mounted on the handlebars,
and you would use one servo for throttle and one for each
of the two wheel drives for steering.
I would use a transmitter with a built in mixer and set it up
so that TX Ch-2 (elevator) is sub-trimmed to +50%
(so it's centered) is mixed with
RX=50%+Ch1 and RX=50%+Ch2 so that moving the stick forward
or backwards makes the mower move forwards or backwards.
With TX Ch 1 (Ailerons) subtrim=+50% (so it's centered) and
RX=50%+Ch1 and RX=50%-Ch2 (note opposite signs on mixing)
Then when you push the stick right, the left wheel goes faster,
and when you push the stick left, the right wheel goes faster.
TX Ch3 would go to the throttle servo.
Now all you need is a lawn chair and a cooler of beer.
BTW, I would put a kill cord around the outside hooked to a
kill switch so that if you lose control it will stop when it hits the car.