the ground wires should not ever be switched through the transfer switch.
the ground terminal on your shore cord is extra long it makes the ground connection first when you plug it in you do not want any interruption of that through the transfer switch. all grounds go directly to the silver ground bus only.
i would put a jumper between the aux and neutral connection on the shore input and leave the same jumper on the control panel output that way the now 2 neutral contacts can handle the full 100amps of the shore power cord. 50amps from L1 and 50amps from L2.