My Part inserts some content into the EclipseContext and then triggers the Addon.
The Addon seems to have a different Context, than Parts do. Is that true?
How would a Part communicate with a Addon?
Anything implementing MContext will generally havens own context.
Addons are held at the application layer, so your part could traverse its container and then search for the appropriate addon. But remember there may be multiple instances of your part, depending on how many windows you have in your model.
A different way might be to use the context's notion of active variables to try to decouple your addon from your part.