Rolling the rope of a kite
It appears from your question development that you are considering something other than the typical &quot;children's&quot; kite in your project.
Your additional information indicates that the aforementioned Spectra line would be a good choice. Light weight, low volume.
My use of the line was for a tow system to launch paraglider and pilot to about two thousand feet AGL. 700 pound test was sufficient to do so and about five thousand feet of line was needed, as the winch pulled in line as the paraglider and pilot climbed.
The winch was constructed from a Yamaha motor scooter, one with an automatic transmission, which adjusted for the load by reducing the internal gear ratio. The rear wheel was removed and flanges were added to convert it to a winch drum. This is not too far off from your thought of using an automobile, although it was easier to move a trailer with the scooter mounted.
Critical to the design was a fairlead to ensure that the line was pulled straight from the drum and returned in a straight line during retrieval.
You will want to consider the winch drum as your start point and build from there. Bearings, axle, support members all will attend to the one-sided aspect of power. If the magnitude of your project is as great as it seems, you will not have sufficient power to retract a kite by using an electric screw driver.
There are many electric bike kits on the market and you may be able to use a higher powered motor from one of those. A number of benefits also apply in that you'd have a controller plus the bearings and axle incorporated in the design. A sturdy frame, perhaps more sturdy than a conventional bicycle would provide the support members.
The rim could be supplemented by flanges turning it into a winch drum of substantial diameter. It may be necessary to use a gearing system from a motor in order to get sufficient torque to retrieve a kite under some high wind conditions.
Note also that wind gradient is a factor for high flying kites. You may have light to moderate wind at ground level, but as altitude is gained, the kite will experience much higher levels of wind. This is caused by the reduction of friction with the ground as one gains altitude.