Alon, most newer aftermarket alarm systems have a neg and or pos signal terminal for incorporating the power door lock systems. If your system does have this feature you may be able to use it to send a signal to the factory door lock system to open with the alarm disarm/Arm via the alarm FOB. Unfortunately I dont think the alarm module has a hard wire input that can be used to turn it on/off. You could set it up using the alarm but usually not the other way around. Look thru the manual that came with the system, see if it shows a input-output connection to manually arm/disarm the system. If it does then you may be able to tie it into the factory system.
If not and your really set on it working this way you could take an extra alarm FOB and cannibalize it into a circuit board so when you activate the factory FOB it sees a signal form the factory power door locks or the Central Security Module that would activate the board to pulse the hardwired alarm FOB turning the alarm on and off.
2001 Ranger Edge 3.0 V6, 5 speed M/T
Limited Slip Differential, James Duff Traction Bars
Kumho 30x9.50 15 MT / Black 297 Series 15x7 Rims