I guess we're looking at the bearing cup with the right hand thread, which still has its dust cover screwed onto the end of the exposed thread.
Let's leave aside the discussion about which side this should be on (probably the right side of the bike, according to the literature, but in your case it seems to be on the left? - the only way to fix this would be to respoke the back wheel, and that would take an afternoon).
When the bike is running down the road, well-greased and well-adjusted balls won't exert too much torque on the bearing cups, so it should be possible just to tighten the cups appropriately to stop them loosening or tightening, regardless of which way the hub is fitted to the frame. Here' my suggested plan:
1. Go back and read
https://www.douglasmotorcycles.net/index.php?topic=9247.0 and understand how the hub goes together.
2. Buy a little bottle of a stong Loctite threadlocker, and a bottle of Loctite primer.
3. Strip your back hub and bearings and clean everything as if you are about to operate. Use an old toothbrush and a solvent to get all the oil/grease off the thread.
4. Examine the balls. If they are at all marked, or more that a couple of tenths of a thou less than their nominal value (0.250"?), buy new ones. There's an ebay seller in the US who does loose high-quality balls - beware of rubbish.
5. The right-hand-thread cup is designed to screw into the hub dead tight, and is not adjustable. It is tightened by a tool with pins that engage into two of the four holes on its outer face. Note that if the dust cover is still in place you can't see the pin holes so remove it if you can. (You have probably already used the dust cover to screw the bearing cup in, in which case it might be jammed on tight, particularly if you used a screwdriver and a hammer to tighten it.)
6. Read the instructions on the loctite. Prepare the inner and outer threads with the primer, apply the loctite, screw in the bearing cup until it bottoms, and tighten it dead tight with the pin tool, or (as most people do!) with a pin punch and a hammer. This should never, ever move again. There should be a few threads of the outer sticking out of the hub - the dust rover can be screwed on later and just nipped up.
7. Grease the balls and insert them into the bearing cup that is now fixed in the hub. Use your imagination and choice of tools. (You could have the balls already greased into the cup before you install it into the hub, but be careful not to grease anywhere near the threads you are about to loctite.)
8. I have mixed feelings about using loctite on the other side. It has a locking ring, so I wouldn't normally... Fit the axle, remaining balls, and left-hand-thread cup. Screw it in until there is almost no play and the wheel spins smoothly. Fit and tighten the lockring. Things ALWAYS move at this step, so it might take a few tries to get the adjustment correct. There must be a very small amount of play (or "shake") in the wheel measured as the rim. Say 1/2 mm (0.020") or so. Just enough so you know that the balls are not binding as the wheel spins.
9. Make sure the lockring is tight - I hate to say it but a pin punch and a small hammer is probably OK as it has probably been used before.
Good luck.
Leon
