On the question of charging both the coach and the starting battery's. Many coaches will not do that. I just made a jumper out of #10 wire and ran it between the starting and coach battery's. Worked just fine.
You said it was raining pretty good. With that information I am going to say you may have sucked in a bunch of water which momentarily made the engine go rich and the white smoke was steam as the water went through the engine.