If you are distributing or

If you are distributing or exhibiting the video, then yes, you do need the permission of everyone living who can be identified in the video. A letter of introduction from the family member that is comissioning the work should be all that’s needed to get the people appearing in the video to agree.

If you are making a one-copy video for your client, like a personal family history, and you have no intent to distribute or exhibit the video (except to your client), then permission is probably not required.