Drive Shaft Brake/Parking Brake works only in one direction

It's probably a simple matter of adjusting the brake shoes. As already noted, you need to be able to turn the drive shaft to get a feel for the correct adjustment. I just lift the rear tires off the ground and support the MH with jack stands. Also you'll need to have the transmission in neutral for the brake to be in the released mode. If memory serves me correctly, you'll need to have the ignition key in the on position also. Look at the brake drum and you'll see a removable clip. Remove the clip and turn the slot to the top to see the adjusting star. I adjust the shoes as tight as I can and then back off the adjuster until the brake drum turns free.

Richard

It may well need a new shoe (Though LOGICALLY it would work the same in both directions it is possible that a new shoe (Replace both) may be indicated

It is also possible that simple adjustment is all you need. This is not the easiest task but basically tighten up on the yoke a few turns at a time till either you get resistance (you need to drop the drive shaft to check for resistance) or they work right. If Resistance re-shoe.

I have a similar MH and the brake holds good in either direction. I am not positive but I think there is an adjustment for the Autopark brake. If that does not work you probably need new brake shoes or possibly something else is wrong.

No, it should hold in either direction. In fact it's part of Wash Dot testing to try and let the clutch out with it engaged (assuming manual trans of course). It should stall the engine when doing so.
I would let him change it.