The summing amp can be a single stage with 50K feedback to give unity gain.
The photodiode cathodes go to a positive supply! They work in reverse bias (photoconduction) mode.
The current through the two photodiodes should be identical, or very close, for any reasonable level of LED current.
That's how the coupler works; the driver opamp sets whatever LED current is needed for the voltage across the load resistor to equal the signal input voltage.
With matched photodiodes in the device and equal load resistors, that same voltage will appear across the load resistor on the output side, so duplicating the input signal.
You could add an inverting differential amp after the original circuit output, to remove the added offset. The offset only needs to be eg. 1V to keep the signal fully in the working range of the circuit.
And be sure to use opamps with very low input currents!