Reversing a 110v circuit instructions

I have a remote controlled gate that has an override switch that people use that don’t have a remote in their possession. The override is a single pole 110 light switch. When engaged it will allow 110v power to run the motor of the gate. When not-engaged it allows the motor to free spool so the gate can be pushed open by hand.
I need to be able to reverse the 110v light switch so the motor re-engages and will open the gate. (this will allow the ladies in their high heels to re-engage the gate without getting out of their car)
I have a 202U, 2 remotes, 12v power supply and a 110v relay that reverses contacts with each activation.
How would I wire it up so that in the case where the 110 switch is open, a press of the 202U would activate the relay to the opposite position and give back power to the 110 switch?

Thanks for your help on this!!!
John

Hello,
By “reverse the 110v light switch”, do you mean simply switching the on/off status of your light switch?