Alrighty..
Well lets see here.
The Grey wire is the power for the light in the switch
The Black wire is a ground for the switch and light
The white wire is constant 12, and depending on the ground the switch gives it, it will either lock or unlock the doors.
Here's what you're going to have to do.
I'm assuming the unlock command on the alarm gives power, so you'll need a couple relays.
One relay needs tap into the white wire, and CLOSE when the lock button is pressed, and the other end of the switching part of the relay goes to ground. That will make them lock.
For the next one, unhook the switch's harness and OHM between the white and black wires and press unlock. You will get a resistance.. NOTE IT. Then get a resistor with that certain ohm rating.
Now, use another relay and tap into the white wire again, use the unlock wire from the remote to power this relay up and CLOSE it when the unlock button is pressed. The other end of the switching part of the relay needs to go first through your resistor, then to ground.
That's how it'll work according to this picture, I drew in the extra wiring for you to hook it up. The relay pins are the correct numbers.
Have fun