We have a small group 24 battery that came stock on our camper, it will give us a hair over 2 days regular use before going low enough to cause "check" light on fridge. We are not easy on it either, lots of water pump use (showers), laptop/cellphone charging, only thing we did to ease our power usage was LED lights.
If you are only getting one night, and only reading 11v after a day of charging, it is definitely a bad battery, one (or more) of its cells are bad.
I have been pretty hard on my battery this season, I know I will be going with 2x 6V GC2 batteries for next season, so I've not been too concerned with damaging this crappy tiny factory battery.