Generator/Shore Power Work, Battery Power Doesn't

So I've tested the voltage while hooked up to the shore power and it hasn't gotten above 12.6. I've tested it with the generator as well and it'll charge a little bit but probably never get above about 12.6 either. The only time it charges that high is when the van motor is on and its charging from the alternator. Is the next step finding any circuit breakers and replacing them? Or do I find the converter and is there a way to test it?