Common DC ground with two bridge rectifiers
While I have not run any time-based analysis of the described circuit, I see a problem with the ground connection. As you suggest, ground connections are used to connect ground of multiple isolated rectifiers or other floating supplies. However, since both rectifiers use the same input pin (3), they are not isolated from each other.

Since the shared connection creates a virtual node at which voltages at location 2 and 4 are phase-shifted by 180 degrees, the two rectifiers indeed do not work as intended. Try connecting one input between 2 and 4 and the other one between 2 and 3 and see if that would work for you.

Flybacks converter with multiple outputs have usually multiple galvanically isolated winding.