The issue is that the source data is stored in XML, not in the database. So your third party software is modifying a copy of the data; there's no way (that I know) for the third party software to edit the xml and resubmit it to the Qdabra web service. Throughout this process, DBXL is the "owner" of the XML, the XML is edited via InfoPath, and the XML data is used to map everywhere else (SharePoint and SQL).
One option (in theory, I haven't tried this) is to change your InfoPath form so that it queries the SQL table on load (to get the latest values), but this requires a lot of work. Even then, SharePoint won't be updated when the 3rd party software modifies SQL. That will only happen when the XML is resubmitted via InfoPath.