I think you need a bigger battery. 7200 W at 24 V is 7200/24 or 300 Amps! So a 100 Ah battery will power it for 1/3rd of an hour not 3 hours.
This is also in an ideal world where the inverter is 100% efficient and the batteries deliver to their rated capacity without drooping low enough for the inverter to drop out. Given the high discharge current, I think you'd need to go considerably higher than the theoretical capacity to make it work in practice and 300 A of continuous draw from a 100 Ah battery is not trivial. I would expect it to need to be quite a special battery for that to work without it getting exciting. Even vehicle starting batteries only sustain that for a few seconds at a time, and their construction for short term high current use makes them unsuitable for cyclic applications such as this.
If you want to charge the batteries from 12V then yes, you'll need to effectively switch them into a parallel combination and put them across the vehicle alternator. You can't do this without breaking the series link between the batteries.
To be honest, I think a generator would be the best option, and probably much more compact than the batteries that would be required to guarantee operation for 3 hours.
I'm assuming this load draws 7.2 kw constantly, of course. If it's only intermittently that might change things.