There's lots of reference images around
tweaking is proving a little tricky, although I've pretty much stabilised the design of the model now so this should help. As the construction is pretty much made up of distinct components, there are usually only one or two nodes that need to be adjusted at any one time. I've added a fade shader to allow for fading of the rainbow from the center to the edges.
I also haven't tried a render with GI yet, and it will be interesting to see what effect the rainbow has on the surrounding rain (possibly not much for thick rainbows). This may help soften things up a little.
My trig was not as rusty as I had thought, once I got the angle calculation correct the automatic calculation of the anti-sun vector worked (I had dropped it earlier it for a manual vector just to be sure). I've left the manual node in as a fallback in case it provides a minor efficiency boost for a stationary sun). The coordinates are calculated based on a 1 meter vector in the XY plane pointing towards the sun. At least now the rainbow is effectively attached to the camera so you can go chasing rainbows around your scene.
Below is the current node structure, which is simplified a fair bit from earlier versions despite doing a lot more. It's also easier to locate specific controlling nodes. The bulk of it consists of just colour adjust nodes that are added or multiplied together.
I'm running another test render at the moment of a complete double rainbow with "rain" and background clouds but it's going to take a little while. I can already see things that need tweaking but it will be good to see what else is working...