"Just parking" between would not be possible without putting really a lot of energy into maintining the position of the shade. Due to orbital speed differences depending on the distance to the sun[1] and the pressure of the light[2] and solar wind[3] on the shade and Earth's gravitational interference. And the shade must be very much larger in diameter than the planet in order to cover it. How large depends on the distance from the planet.

[1] See https://en.wikipedia.org/wiki/Orbital_speed#Planets

[2] See https://en.wikipedia.org/wiki/Radiation_pressure

[3] See https://en.wikipedia.org/wiki/Solar_wind