I'm still convinced that it's an issue with the charger itself but I'll entertain the thought that it is working fine. The easiest way to have the battery disconnect from the load would be a NO relay that simply trips at a voltage because there is not enough to keep the coil energized. That would still create the problem though that it is using power just to keep itself closed, and as soon as the battery is set to charge again, it would re-close which, as you said, is not wanted. The next best way to do this is to have a comparator to monitor the voltage and trip at a voltage that is too low. I already gave you a part number, the ICL7665 is good for 1.6V up to 18V so it can easily handle the job. As for the FET that you want, I am unaware of any FETs that are bi-directional. You can make a bi-directional FET switch by simply connecting two FETs in opposite polarity of each other. Try to avoid using a power MOSFET though since most of them have an internal diode to protect them from high voltage spikes. This diode would create a short across the opposite FET, and your switch would be completely useless.