Multiple Wireless charging coils (Qi) in parallel?
Qi wireless charging relies on coupled LC resonators (Inductor in parallel with a capacitor).

Your diodes solution will not resonate so it will not work.

Besides that some communications happens when you place the receiver coil on the transmit coil by means of shorting the receiver inductor. This also cannot happen in your diodes solution.

You will need a separate Qi power receiver and coil on each side of your device.