Installing JDBC drivers as library jars is really not the right approach you should be taking, but anyway, you find a line like below in read-config-variables (production Rhino) or config/jvm_args (Rhino SDK):
If you uncomment that line and restart the node, the Java security system will dump lots of debugging information about security accesses. When your access control permission failure occurs you can find out which protection domain failed the permissions check.
Given that it appears to be a thread started by the JDBC driver that's failing the permission check, resolving this might be difficult. Using a AccessControl.doPrivileged() block around the code that starts the thread(s) might work, if you know where that occurs.