It is probably the batteries.
You said that you haven't had any trouble with them yet. How often to do you check the water levels in the cells? I bought my trailer from a guy who kept it plugged in almost all of the time. The batteries were only 3 years old but 3 of the cells were completely dry.
And, if you let a battery get down to 10v it is almost impossible to bring it back to a full charge and the life of this battery had diminished greatly. Hooking up a weak battery to a good battery will only hurt the good one. It is one of those weak link arguments.
I would check the electric brake, I would turn off the defroster mechanism on your dometic fridge and then get two good deep cycle batteries. Don't get marine batteries but genuine deep cycle batteries.