2 chargers connected to one battery bank?

Given that smart chargers vary the voltage throughout the process, and that dumb ones do not, this suggests to me that having both a dumb and a smart charger on the job at the same time would be a bad idea. I can see the smart one throwing 13 volts at the other one that is putting out 12 volts, thus having the lower voltage unit force fed current backwards. Charging a battery charger is not what they were designed to do. I'd anticipate possible overheating and circuit damage.

So I'd say one or the other, mate, but never both.