iRig Pro Duo will work with non-iRig microphones. If you are trying to run both apps at the same time you will not be able to unless you instantiate them in an iOS DAW app or similar (using either Audiobus or Inter-App Audio). But also, for multiple inputs like iRig Pro Duo, there's a setting for multitrack recording in VocaLive that you would also need to make sure is set or I don't believe the second input will work at all in there.
Beyond these suggestions, the IK Support team would be best equipped to help figure out that else might be going wrong to cause you to not be able to do certain things with IK apps and interfaces. They can be reached via
http://www.ikmultimedia.com/contact-support