car stereo powering from the mains

Guys I need your help here.

I currently have a large stereo in my project car which features 2 x 12" subs, 2 x amps, 5 x tv screens, dvd, car pc and neons. i do have a large leisure battery powering all of this in the rear of the car as well as the battery in the front. The two are connected through a split charge realy.

Recently i have been connecting a trickle charger to the rear battery so that i can run all of the kit at shows for long periods of time? I have noticed however that the charge going into the battery is less than what is being consumed and the battery goes flat after a few hours, forcing me to shut a few things down.

Is this the right way to connect the car to the mains, or will this just overcharge the rear battery?

Could you recommend how to get around this? and any kit i may need?

Thanks