Sub-projects are a great tool, but the redmine UI needs some polish to make switching between them more fluid.

Redmine should use a hierarchical hyperlink as its project title. for an example, look at pretty much any forum with sub-forums: http://forums.cgsociety.org/showthread.php?f=89&t=525100&page=2 Notice at the top where it displays the hierarchy of sub-forums:

CGTalk > Application Specific (3D) > Autodesk Maya > Maya Programming

So the title displayed in the top-left corner would be

Master > Sub Project > Sub Sub Project

and "Master" would be a hyperlink that takes you to the "Master" project page.