The way you are operating you could easily get by with 1KW generator. A 2KW might even run the HVAC you have attached to TT.
As far as recharge time for the battery, how long does it take to recharge battery on shore power? It will be the same for your TT on a generator.
We call our TT "our lifeboat." That is to say when the power fails at home we fire up the gensets and stay in the TT. If we think parish water might run short, we fill the tanks though we have additional water filters and a swimming pool.
Without the gensets we cannot run the AC or the pardette's hair dryer. We don't need it for the pardette's coffee maker because we have an old west coffee pot.