Welcome to TSG!
ATT????.Dat (Numbered attachment data) files are created by Outlook for attachments when Outlook is not configured properly (I'm don't know what that is though). Is you family sending these as actual attachments, or are the inserting them into an email? If the latter, they may be in a format that Outlook can't understand, so instead of placing them "inline" they get wrapped into an Attachment.dat file. It they are attaching photos that are in a RAW format (the camera's internal format) Outlook may not know what to do with them either.
Sounds like some re-configuring on the sending end needs to be done, either in their mail client, or simply making sure the files are in JPG format.
You can use this online tool that might extract the files. There is a 5 MB limit, and you do have to upload the files to their server. I know nothing about the site, just found it on a search, so can't comment on their privacy policies or reputation:
http://www.winmaildat.com/
HTH
Jerry