What about putting a heavy moving type blanket over the roof and down the sides of the shed? You could try covering the shed with insulation and then put a second roof over the top so the chickens can't get to the insulation and so it will stay dry. keep the door on her side closed and put a heavy blanket or carpet on that side? The more sound proofing the better. I would not worry about them getting enough light if the other side is open.
Good luck
Good luck