Is the water pump more likely to work when the generator is running? This could make sense, as when the generator is running the DC voltage is being increased by your converter to charge up the batteries and then the pump has enough voltage to run. However, the pump should work just fine at just battery voltage. Maybe there is something stuck in the pump diaphragm area that is making the motor work hard. If that something kept the pump from turning, it would make the motor get very hot. Or maybe the motor is going out. Or maybe the pump power connections are dirty and need to be cleaned up. Could you battery voltage be very low (say below 11 volts) when not on generator? That could make the pump not work correctly, also.
I think the first thing to check is the battery voltage when the generator is not running.
There's lots of advice and information in forums... sometimes it is correct. For example, all of my posts are made by a political appointee who got the job as a reward for contributions to my diesel bill.
2011 Jayco 28.5RLS; 2008 Chevy Duramax; Pullrite Superglide Hitch