Will this IGBT switch operate correctly?
Your opto output doesn't make sense. All it does is short gate-source without ever applying a voltage to gate-source.
IGBTs cannot conduct in reverse, which would mean either D1 or D2
would be carrying the full current of a particular polarity plus any
associated forward conduction loss. Why are you using IGBTs instead
of MOSFETs at such low voltages? MOSFETs can conduct through the
MOSFET channel itself in reverse for lower losses.
For gate ringing, place a series resistor for EACH gate as close as
possible to the gate.
If it is supposed to interrupt an inductive load, you will need
snubbers across drain-drain.
If you have inherently an isolated supply, consider applying a
couple of negative volts to the gate-source during turn off. IGBTs
can have turn off issues.