I can't imagine why your called party's phone would behave that way, since neither Google Voice nor OBiTALK have any control over it. As far as they know, it's just another phone call. But, if the alarm panel is connected, there's no telling what signals from it might be interfering, or if there is an impedance problem with it in the circuit.
You do realize that an OBi 202 has two physical phone ports? For example, you could have two different Google accounts, each with one Google Voice number. You could then provision SP1 with the GV number you want to use for regular calling, on your primary Google/Gmail account. You'd then provision SP2 with the other Google Voice number, solely for use with the alarm panel. You'd provision SP3 with a SIP VoIP service provider that offers E911 service.
Google Voice isn't intended for this purpose, and use it at your own risk until you can upgrade your communications with the alarm company, but it should work. Note that alarm panels are typically wired into your premises jacks via a special phone jack, known as a RJ-31X "exclusion" jack. This jack loops the telephone line from the telephone company (or from your OBi in your case) through a relay in the panel. Normally, the relay simply passes the two wires' connections through to the premises wiring, but when the alarm goes off, it "seizes" the line by disconnecting the two wires going to the premise, so nobody can take a phone off-hook to kill the call to the central station. This can be confusing to wire, and a mistake could render your panel unable to communicate, and/or your premises phones to not work. It's best to have an alarm technician do this.
Here is a DIY tutorial, so you can at least understand how it is wired up:
https://youtu.be/Z2gcXngLgVE