NameMapping issue with Java application started from Internet explorer.

If the Java version is the same, and using Java Web Start the ID's of your UI controls are the same. Then you should be able to organise your name mapping tree structure like so - creating a new parent node Sys\parent_new and copying the child of Sys\parent_old\page to Sys\parent_new

If this possible solution does not work for you, then you have no option but to recreated all the name mappings again.