Murray Mcmurrray's & Stromberg's hatcheries both have RIR bantams. Although they are both straight run. Many places only sell bantams as str. run which makes it difficult to find just hens. I bought 5 str. run bantams from strombergs and got 3 hens & 2 roosters.
Have fun with your chickens! We buy large groups of egg cartons of the internet. I don't know any thing about automatic doors, but I'm sure someone will help you out. Good Luck :)
I have had chickens for many years and we have always just chased them in and closed the coop at night until they learned. It takes a few weeks but they always eventually go in before it gets dark. I say just give them some time to learn.