Looks like right now there is no way one can pass additional jar files to spark_submit from Zeppelin.The same works fine if I am not using spark_submit option (by not specifying spark_home).
When I checked the code interpreter.sh I found that for the class path it only passes the zeppelin-spark*.jar available in zeppelin_home/interpreter/spark directory. I suggest to put this as a bug/enhancement. The solution should be pretty easy by making some small changes in interpreter.sh (I've done the same and could make it work with some external_lib folder under zeppelin_home/interpreter/spark directory). Regards, Sourav