From what i see in your specs, yes you do need a DC-DC charger. In fact you need the biggest amps one you can get to be able to recharge 220Ahr in a reasonable time. EG if you only had a 20A unit it would take 6 hours driving to recharge half that capacity again if they were half flat.
If it was mine I would be backing it up with double or more solar also and get free power while the sun shines driving or stopped.
If you have a caravan I would use a DC-DC charger.
Stick your multimeter on the starter battery while the engine is running, should be close to 14.4 volts & then on the caravan battery still while the engine is running. If the voltage is less than 13.7 volts get a DC-DC charger.
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Get Atleast a 30 amp charger . I fitted a smart 50 amp . The generator doesnt run very long before we have charged batteries on bad days . Most the time its charging much less amps being 7 stage smart !! Generators normally just supply 12v not really for charging !!
EG if you only had a 20A unit it would take 6 hours driving to recharge half that capacity again if they were half flat. 
