Is it generally possible to access a shareable interface of an applet installed in a different Security Domain in a card compliant to both Java Card and Global Platform specifications?
If this is not possible, is there another way of invoking applications in another Security Domain, potentially by manually communicating via Secure Channels?
From the JavaCard Runtime Environment spec, Shareable Interfaces (6.2.4) :
Shareable interfaces are a feature in the Java Card API to enable applet interaction. A shareable interface defines a set of shared interface methods. These interface methods can be invoked from one context even if the object implementing them is owned by an applet in another context.
The applet firewall of the Java Card world divides between contexts(6.1.2), the ShareableInterfaceObject is spefically designed to enable interaction between contexts that would otherwise be forbidden.
The concept of Security Domains originates from the Global Platform specifications and is not present in the JavaCard specification. Searching the term in the JavaCard documentation will actually yield no results. As these things don't have anything in common, there should not be a problem with your setup.