Many good replies here already but I notice you say the gas doesn't
start up till the water is already cool.
It should not be like that.
It's possible the gas heat thermostat is defective or not in good
contact with the tank.
You don't mention your brand and model number but some
brands you can purchase a hotter thermostat from the factory
or a well stocked parts dealer.
Mine has a totally separate thermostat for the electric and another
for the gas. This is typical for most RV water heaters.
The electric will always come on first but if we
use much water the gas will come on pretty quickly.
I gotta be honest, since we camp a lot in Kentucky state parks
and they usually have pretty decent bath houses we usually
don't shower in our trailer so this is not an issue.
While on our big adventure out west this June I did shower
in the trailer a couple times but the old "navy" shower was
the order of the day because we were dry camping with no
sewer and no water hookups. When you take a 5 gallon shower
in June you don't use a lot of hot water