The battery will be fine at work for 10 hours. Same as the battery (near full charge) will be fine overnight while you sleep. If your generator can start and run both A/C the fridge will be a minor blip. Worst case the included inverter will start/run the fridge direct if you turn the breaker off to the branch circuit that feeds the fridge.
Depending on your experience and usage patterns you may want to eventually add solar and another pair of batteries.
If the RV comes with a WFCO converter you might need upgraded charging sooner than later. WFCO is notorious for a slow charge at 13.6 volts and not going to boost mode (14.4v) when expected. If you are running the A/C 12+ hours a day this is less of an issue.
