I suspect your problem is that you've somehow created  the PROD and DR
environments as exact duplicates of each other. You can have multiple  paths and
jobs from a single staging  site, but the destination  has to be different for
each path. If your DR is a restored backup of the Prod server  you won't be able
to use Content Deployment to deploy to it. If it is built as a separate but
equal server then you can deploy to it from a second path  with the same starting
point.

This issue happens when I am creating a new path.

Do you mean if I delete the site  on the DR box and create  a blank
site, this would work?
Or do you mean something different,, please explain.

How were the PROD and DR environments created? If they were restored from the
same backup into different FARMS then that is the problem because they have the
same GUIDs for both the source and destination  as an existing Path.

Other than that, the destination of a new Content Deployment path  and job must
be a Blank or empty site.