I have some garden helpers who are removing the big old rhododendron at the lower right end of my garden. Its a several day project to chop it into pieces and pack them into garbage cans for removal. The bush was shading my tomatoes and potatoes quite a bit, so I finally decided it should go. It turned out to be a fun project for my garden helpers who just happened to have a new saw-type tool to try out.
My dad has looked into composting rhododendrons for me and the answer is – don’t. The plant is toxic and compost from it can be detrimental to plants and soil microbes that would grow in it. In general, it seems to pay to be careful what you compost in the way of clippings and shrubs as many common ones are toxic. A list is here.