You're making an erroneous assumption which then is causing all your problems.

Your assumption is that the system inputs drive to the sun gear, but in fact the Sun is usually fixed to the axle as the fulcrum of the system, and the drive is input to the cage in which the planets are pinioned. Now as the planets revolve around the sun they are forced to also rotate so they drive the ring in the same direction but faster than their planetary cage, accounting for the high gear.

The middle gear is via directly driving the ring (output gear) bypassing the planet system entirely.

The low gear is achieved by running it backwards, inputting to the ring and and outputting from the planet cage.

How gears are selected is via clutches which determine which is connected to the sprocket or hub shell at any time.