well, sounds like you have TWO seperate issues, if the tow vehicle's battery
discharged .... I would verify the alternator is working properly, any battery store can do a couple quick tests for you on this, most will do them for free...
or use a digital volt meter. measuree the battery voltage after the car has been parked a couple hours.... if the battery is close to fully charged, it should be around 12.6V. now start the car and measure it with the engine running, it should be about 1-1.6 volts higher, like 13.6-14.2V
measure the trailer battery with the volt meter, ditto if its fully charged, it should be around 12.6V. deeply discharged, 12V or a little under. plug the 7-blade in, start the car engine, you should see 13.6-14.2V charging voltage. (but if the car isn't charging its own battery, fix that first, you likely need a new voltage regulator or maybe an alternator, or maybe a new belt).