Andy,

You can also import a new certificate on all computers running the applet via the Java Control Panel. See http://docs.oracle.com/javase/6/docs/technotes/guides/deployment/deployment-guide/jcp.html#security

When I did a little more research, it looks like InCommon certificates have been trusted by the JRE since v1.4.2. See https://spaces.internet2.edu/display/InCCollaborate/InCommon+Cert+Service+FAQ#InCommonCertServiceFAQ-Whatarethesupportedbrowsers%2Cdevicesandapplicationsuites%3F

I wonder if there is a SSL configuration problem on your server which might be causing this problem. The InCommon documentation says this type of behavior might occur if all the InCommon Intermediate certificates are not properly installed on the server See https://spaces.internet2.edu/display/InCCollaborate/InCommon+Cert+Service+FAQ#InCommonCertServiceFAQ-WhyisthebrowserrejectingmySSL%2FTLScertificate%3F for description of what the problem might be and steps on verifying that the SSL certificates are configured properly on your server.

Brian