How good is your "good" 12V source? The starter likely needs more than 100A to turn over at first. Maybe the ground between the starter and the generator or the generator and the motorhome is not sufficiently good?
I had somewhat similar symptoms for my generator (an Onan 4KY), and it turned out to be the starter motor (and replacing it cured the problem). The actual fault with the motor was one of the four brushes was disconnected, making it run at half power, which was barely enough to get my generator to turn over most of the time. Eventually I burned out a winding or two on the rotor of the motor when it was a wee bit harder starting due to cold weather, and so had to replace the starter. On the 4KY, mucking with the starter motor requires dropping the generator for access, so it's a good bit of labor for an otherwise straightforward repair.
