jackrae:
Let's go back a few stepsQuestion - Why do you think you need a 3A regulated supply ? What is your actual load ? Just because the power supply can provide 3A+ doesn't mean your regulator has to be rated at that figure. If 6 volts meets you back-up needs than "losing" 12.5 across a linear regulator is a shear waste of power (12.5 x 3 = 37.5 watts). If you really need 6 or 12 volts (you seem to be a bit mixed on voltages) then I'd suggest a switched mode regulator that offers over 90% efficiency with very little heat.
I have a solenoid lock,alarm,relay rated at 12v. A couple of 5 inputs to arduino. The gsm shield required is 1.5A. Assuming the arduino is 500mA, gsm is 1.5A, the solenoid lock is 200mA, alarm is 300mA, relay is 50mA then the total is 2550mA or 2.5A. The remaining 500ma is just for extra. The purpose of the back up battery is not to power them all but to only power the arduino and gsm, so that the gsm can still send message and call.