Shut the door!
This happened to us last week. It's actually pretty easy to fix. The door mechanism is made by TriMark, but you don't need a anything but a screwdriver and hammer to fix it. The trick is getting it back together properly. MarkJUrban is correct, it is just a press fit. (Cheap way to make it, IMHO.)
All you do is remove the 4 screws of the black panel that the door handle fits into - it's on the inside of the trailer. When you do that it's likely that the "D" shaped piece falls off, since the press fit failed. So, put it back together, and make sure the door lock slide is in the unlocked position. The handle should be positioned relative to the panel so that it would be parallel to the floor if it were in place, and that "D" piece is placed with the two little legs pointing down towards the floor.
Take a hammer and pound on the edges of the square so that you flare the metal a little bit, creating a new press fit. Now all you have to do is put the panel and the handle back on with those 4 screws.
The tricky part is getting the feet of those little legs in the right place in the mechanism so that the handle works again. This is difficult to describe and impossible to actually photograph, but the notch that is cut to make the little legs is there for a purpose, and you have to get each leg on one side of part of the mechanism. The location of the holes for the 4 screws will more or less tell you where it goes.
We no longer use this handle to close the door from the inside. The handle on the screen door works just fine to close both doors.
But, as I said, this isn't a terrific design. There is a little hole in the middle of that square part of the handle, and that should have a screw that holds a little washer to hold the whole thing together. But, I don't know if there is room in the mechanism for all that. My plan it to take it apart again and reinstall it with a little bit of putty or clay with a piece of plastic wrap on it (so it doesn't stick except to one side). I'll put the panel back together to squeeze down the putty, and then take it apart again. The thickness of the putty will let me know how much space there is and whether I can put threads inside that little hole and fit it with a metal screw and washer. If there is no space, then this won't work of course. . . . . and I'll have to think of something else or just live with the risk of it failing again.
BTW, your indication that the handle is about to fail is that the door handle seems a little sloppy.