You are best to use whatsap or Skype or similar, as mms will severely limit the size and quality of the video. You can go to some cafe etc and use free WiFi if you are very limited with data...
Depending on how big the video file is in megabytes, your best bet is probably to upload the video to a file sharing site (dropbox.com, google drive) or a photo hosting site then messaging the URL of the uploaded file to your family.