keyless entry negative trigger issue

It may be possible to repair the alarm.  Quite a few alarms use one (or two) darlington transistor chip(s) for all the (-) outputs.  This is typically a through hole mounted chip that is readily available (made by Toshiba).  I haven't look inside an Audiovox alarm lately though, but it may be worth opening it up and taking a look.

Are both the (-) and (+) output bad?  If that is the case, it may also just be a burnt trace on the board, something you can fix by soldering in a jumper.

How about something like this:

It uses three 200mA transistors that are easy to find.  You may have to play around with the resistors a bit but they should technically work (capable of ~500mA output when transistors can only dissipate 200mA)

The top PNP transistor will "trigger" on the (-) pulse while the bottom transistor will ignore the (-) pulse.  The top transistor will output 12vdc to the second transistor shown.  The second transistor (NPN) will trigger and output a totally isolated (-) signal.

The bottom NPN transistor will trigger on a (+) pulse while the top transistor ignores the (+) pulse.  The NPN transistor outputs a (-) signal so it can direct drive a relay.  You will need to protect the transitors by placing diodes across the coils of any relays you drive.

If, for some reason, you need to drive more then one relay off of each output you most likely will have to drop the resistor values down (to 470 or so).  While technically you will be over driving the transistors current capacity they should be fine due to the fact they are only on for ~0.8 seconds at a time.

I've never tried this, but I do think it will work.