If I remember the 100w Renogy system will put out about 5 a/h. The only thing in use during the day may be cell phone chargers and possibly a radio and the water pump. So on a decently sunny day the battery should stay 100% charged by sundown.
Thinking more about the inverter set up, and looking at
this 12v TV. At 39w / 12v = 3.25 a/h draw so for say 2-3 hrs of TV we should be fine.
Thinking about how we used the inverter in the TT, it was really only for the TV, so I'm thinking a 12v TV will save the overhead and expense of the inverter and transfer switch. All our devices are chargeable by USB.