Do you own or rent the property?
If you own, why not a self-supporting awning attached to the structure? Depending on the construction, etc, you might have to consider supporting on uprights attached to the ceiling joists, and cut some roof tiles for them to come through (easily weather-proofed with flashing, etc).
Something like these retractable awnings might do the trick. Not cheap, but easily done, and shouldn't even require a permit, depending on the planning rules in your city council. I know of models that have sun and wind detection - they come out automatically when sunny, and retract automatically when too windy.
If you rent, or cost/installation is an issue, then maybe find the largest cantilever umbrella you can?
My first thought is to build it "too big" - like 2 posts at the hedge on the right and the other two near the windows. Now you have shade for double the vehicles. Those posts aren't in the way and shouldn't impede much - as long as the horizontal beams aren't too low. On second thought it might be a very expensive couple of beams to make that long span work
