Pretty tough without getting in the internals of the portal.
Do you really need this to be two portlets? Why not just a single portlet with two views, and a mechanism to determine which view to show?
I agree with Peter it is a good idea however it would require some state management from the global portlet in order to avoid collision between render parameters, session attributes, etc...
Thanks for your help!
I've just decided to open portlet B in a popup window.
That serves the purposes.