That driver should run up to 18V supply and still work from 5V logic input OK. Shame it blew up - you don't appear to have heat sinks on the FETs, this is not good...
I warned earlier about testing with limited current and watching for problems before applying heavy current. A lead acid battery can source huge currents and won't forgive any mistake. Suggest testing with a more modest voltage and current limiting, then if all well increase voltage, then increase the current limit and test again.
A series of 12V car bulbs can be used as current-limiters - 5W for low current, higher wattage (like headlamp bulb) for higher current testing.