You can bind to both interfaces (see http://wiki.jboss.org/wiki/Wiki.jsp?page=JGroupsUDP) but I highly doubt that's your problem. What network the inter-server clustering traffic runs on is unrelated to what network the client requests are running on. You say App1 fails over; I assume you mean that the session is replicated and available on the the other server. If so, that means session replication is working and there's no reason it shouldn't work for App2 as well.
Suspect either you have a load balancer issue or App2 is not configured for session replication ("distributable" element in web.xml).