Ok well first a couple things - it has nothing to do with the brake system, service or emergency, but braking (forced deceleration) may be creating a situation which contributes to visible oil smoke, causing some confusion there. Your black cloud is just unburnt fuel during initial acceleration and unrelated to the problem.
Also I’m guessing the engine brake is a Jake (compression) brake and not an exhaust brake (has a high/low or high/med/low) - is this correct, or is it just on/off?
Two possibilities are rings and the crankcase vent system. It would be good to have someone follow you around a bit to get a better idea of when it smokes and how much. They will be able to see a lot more than you can from the driver’s seat.
A couple questions:
1. Any oil noticeable in the exhaust system?
2. How long have you owned the coach and is this a new condition?
Also you might add “smokes“ or “smoking” and “2003” to the title to get experienced mechanics interested, and note the manufacturer and model in your next response.