What about if you put the door about 5' from the ground. More like a window then a door. Instead of having it low? You could put a perch under it so the hens could fly up to the perch to get inside.
Or cut one of the existing door in half so the top and bottom both opens.
Easier yet, when the hens go in for the night, feed them then. When you let them out for the day pick the feeder up.
Good Luck!

wow..good ideas! thank you...I like your idea of taking out the feed during the day too...very cool ,thanks xx

Take a piece of plywood (1/2 inch at least for the weight)about 16"x16" cut an 10"x10" square out of the center and put it back with a hinge then cut an 8"x8" hole in the shed wall and fasten your door assembly to the shed with screws or bolts the smaller hole in the shed will allow an overlap to keep out drafts(fudge the measurements as you see fit IAW your chicken size). Mount it inside or outside as you see fit and latch it as you see fit. Couple of pulleys and a string will let you open/close from outside (just fasten a weight to the bottom of the door to hold it closed0 just an idea.

Dave

Can I screw into a resin shed? will I need special screws? what a fabulous idea!

Either use nuts & bolts or run the wood screw through the plastic into the plywood. Just put a big (1 inch +/-) flat washer on each screw and use screws that are just long enough to go almost through the plywood but not poke through. If they do go all the way through, just backthem out, cut the end off and run it back in. You can give the wood a good coating of something ahead of time to prevent moisture swelling if/when water gets between the wood and plastic, or run a bead ok caulking around the seam.

Dave

Great!! Thanks ever so much!! xx