Could we get more details on exactly what you want to do?
iTunes used to be able to do this well if you are referring to within your own home. Also, iCloud Photos.
PLEX might be something to look into if you are talking about multiple homes.
I'v tried Plex, but didn't get it to work like I would.
There are several options. One is to set up your own server and let your family stream from that. Plex is one of the easier ways to do that. But if the Videos aren't too big, you can also upload them to a cloud provider and let your family play them on the ATV using Infuse (which supports Dropbox, Google Drive, and MS Onedrive), or simply on a computer if they have one. Yet another option is to use private Youtube videos.