"Union" joins multiple paths into a single object. If one path is completely enclosed by another it will be absorbed into the larger path. In your case the outer circle encloses everything else, so doing a union results in just that outer path remaining.
What you probably want to do is to select both circles and use Path > Stroke to Path. This will turn each of them into a "doughnut" (or "donut" if you prefer the American spelling) with a very large hole in the center. Use the node editing tool before and after the conversion to see the difference. Now you should be able to union all the objects and give them a single fill with no stroke, rather than the mixture of filled and stroked objects that you have currently.
As an aside I can recommend the Inkscape user forum (http://www.inkscapeforum.com
) for these types of questions, where you will probably get a better cross-section of replies which may suggest other ways to approach your goal.