Personally, along the KISS principle, I'd make a standard full size screen door and jamb, like a million US residences have. Two ways. Build the screen door an inch over the inside yurt door jamb dimension. Make the screen door jamb. Hinge and hang the screen door on its jamb. Screw the whole prehung screen assembly to the yurt door jamb with screws.
Second way. If there is sufficient yurt door opening width (I don't have that) you could make the screened door a half inch smaller than inside yurt door jamb. Or a quater or three eighths smaller if you have a super rigid jamb. Hang on jamb. Add stop for the screen door to close against. With this system the face of the screen door MUST be in plane with the face of the jamb. MUST BE. No questions asked.
If you only want half a screen door, build either of the above, but have the bottom door rail sized to butt into the lower dutch door. Cut it oversize to begin with, install, then cut to fit the closed lower door. Less math that way.
Note. All these screen doors are going to be hinged the same side as the main door but open the opposite swing. If one door opens in, the other opens out.
Any other system is one off, and way beyond the KISS principle.