Number 2 might not be possible if they're reaching the applications through the built in web browser since they'll have the same launcher association in DataWedge.
Hmm this is a tough one but there might be another option.
How are they accessing the web applications? Are they bookmarked, shortcuts, typing in URL bar?
Are they using the same barcode type(s) for both applications?
Is the EMDK being used for any application on the device?
Building on your 2nd option, maybe a pass through application that Modifies/Enables/Disables a DataWedge profile when switching from 3rd party applications might be feasible.