It sounds like you have 3 routers on that network: 2 AirPort Expresses and a Linksys, is that correct? If both the AirPort Expresses are connecting to a Linksys router then they should both be in Bridge mode instead of sharing an internet connection.
(Select Manual Setup for the router in the AirPort Utility application, then choose the Internet tab and set the Connection Sharing option to Off (Bridge Mode) instead of Share a public IP address.)