Remove the seat.
Hopefully, that will give you enough access to the screws / clips that hold the door panel in place.
The plastic piece that keeps the push rod in place might not be broken.
It might have simply came off of the rod.
In either case, those plastic pieces are not expensive.
2003 Wrangler Sahara, 4.0L, Automatic, Stock, Full Metal Doors, Half Doors, Running 31x10.50x15s