the only way to "over charge" a lead acid battery is to apply too much voltage...even the cheapest 12V chargers will not hurt your battery.
Bob. your system would work fine, only add a 7 or 10a fuse inline somewhere in the circuit for short circuit protection. What you discribed is essentially what we do with multiple larger batteries in parallel. Drive around/run the engine to charge the batteries then at camp disconnect the battery bank from the truck battery then run the inverter off the battery bank.
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