Rolling the rope of a kite The base question of the problem is here. Another related question here.
Additional to the material of the rope, I also need to be able to deal with the said rope when lowering the kite, when the fun gets to an end.
Rolling a few tens or hundreds of meters by hand, might be doable. Rolling a few kilometers of rope by hand, should be a serious physical challenge, I guess.
Additional to the rolling itself, some actual force might be needed to lower the kite, as it might not want to come down. Which complicates the problem even more.
Of course, one solution is to have an entire team of people on the problem - which is far from what I have in mind.
The other solution is to have some kind of help (mechanism?) to help me deal with the problem.

I had an idea about using the wheel of the car for this purpose (actually, one of the powered wheels, still attached to the car), but it has several drawbacks. The main con reason is safety related - it is plain dangerous. Also, the car might not be allowed at the site of fun.
I also amused myself trying to find a way to use an accumulator-powered electric screw-driver. The main issue is that it is asymmetrical, the screwdriver being on only one side. And will the accumulator have enough energy? It seems that at least 2 people would be needed in this case also.

Having an entire setup with combustion engines and gears is cool (and more suitable for the Engineering site), but I had in mind something more like &quot;crafting hack&quot;. That is why I added the question here. It also does not really fit in the Lifehacks site, unfortunately.
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.