I cannot tell you why the factory alarm is triggering at one place and not the other but I can tell you that the remote starter is not disarming the factory alarm.
In order to disarm the factory alarm, the remote starter must supply a ground pulse to the disarm wire at the body control module (BCM). The BCM is located in the driver side kick panel and the wire is black in pin "L." To arm the factory alarm, the same wire needs a ground pulse through a 1k ohm resistor.
I have not installed the 1401, so I am not sure if that particular unit has outputs for factory arm and disarm, most DEI products do have at least a disarm wire that is light green/black. This wire outputs a negative pulse that should disarm the alarm without the addition of relays. If 1401 is equipped with a alarm rearm wire it would most likely be green/white. This wire also outputs a negative pulse but it will not be sufficient in rearming through a 1k ohm resistor without a relay. The relay terminal would be wired as follows if the 1401 is capable of this feature:

30 = vehicle black wire (solder in 1k ohm resistor)
87 = chassis ground
87a = no connection
85 = green/white wire of 1401
86 = 12v constant (fused - 5A is more than enough)