No dash lights, abs light on, many tones going off, low battery?????

1999 Crown victoria LX. the battery is always low when these symptoms occur. Not dead but low enough so the car cranks slowly before starting. I also recently (three weeks) installed a tail light converter on the car to run the lights on my trailer. The alternator and battery have been replaced new. Six months for the alternator and last week for the battery.
The car will start and run for maybe a minute the dash lights go out, the ABS light comes on and the bells start to rings, Headlights (if on) will dim or go off completely. The engine starts to miss. The car will drive but if you let the it idle it will die completely. You can drive at high RPM but eventually it will die. At no time either before this or during these occurrences, is there any indication from the car\\'s dash that the charge system isn\\'t working properly.
If you manually charge the battery it will run perfectly for a few days, then all hell will break loose again.
My suspicions are.
1. the new alternator is bad. But with no dash indicator of a charging problem thats strange!
2. the new light convertor is causing the problems with the electrical system?
3. there is a ecm problem. Checked for codes at autozone-no codes present. I\\'m stumped!

First, try disconnect your trailer tail-light converter. You may have something hooked up wrong. I am understanding that this problem occurred AFTER you installed the converter. You may have 1) a wire setup wrong (to ground when it shouldn't be) or 2) the converter is bad.

Once you have worked on this, then you can start looking at the alternator or battery.

+1 if that is the last thing changed eliminate it as a cause.