Based on the image of their hitch that I found and added to your question, you're going to have to modify the hitch to make it work. It's designed to rotate (I don't think that's a good decision, but that's what they did).
If you have enough clearance between the trailer and your rear wheel/mudguard, you could rotate the hitch forward and clamp it to the chainstay. I'd use a jubliee clip (hose clamp), and leave it there permanently. The problem with that is that you won't be able to remove the rear wheel without removing the clamp. If the chainstay sticks out past the dropout it's also going to bend the hitch when you do the axle nut up, which I would not do.
The other option is welding a bump/tab onto the inside of that clamp as described by solson. I strongly suspect that mount is steel, so it's easy enough to weld onto. If you don't have a welder it's going to be 10 minutes work for a metalworker to do it, plus you will need to repaint the hitch afterwards. I would buy a second hitch for this, since Croozer sell them, and that way if you stuff it up you can still use the existing hitch. If you're paying, clean as much paint as you can off the whole hitch (welding will heat the whole thing up and burn off paint over much of the hitch, which is stinky, so if you don't do it you're going to be paying someone else to do it). Then work out exactly where you want the tab and scratch marks along each edge, from the hole in the middle right out and down the outside edge (so they're visible after the weld covers the scratches on the inside surface). The welder will put a blob that extends past the scratches (molten metal doesn't sit in nice box shapes), then you will file it back to get nice straight edges that will lock in place nicely. If the metal place is able, oil quenching after welding will harden the bracket which will be helpful.
What you're trying to get is the red blob added on the dropout side of the hitch, so it sits on the slot in your dropout when the wheel is installed.