As promised here is how I manage to get a coat or jacket on or off as I can't get my arms behind me. I had to sort something out as I live alone and have yet to train my cat to help me out. My Home Help only comes once a week (as I have to pay for her myself) and although my bungalow was designated as Supported Housing they have taken away our Warden to save money and have re-designated the bungalows as ordinary social housing.
I have put strong clips either side of my kitchen door and then hang the coat/jacket up by the shoulders allowing a bit of slack. I then put one arm in followed by the other and stumble forward which releases the clips. It is a bit awkward as I have to balance on one crutch followed by the other but it works, sometimes I need a couple of goes though! To take a coat or jacket off just clip in the cuff of one sleeve and pull your arm out before repeating the other side.