Your family camcorder videos probably weren't made available for checkout at the public library, filed under "young girls doing gymnastics" in the library's card catalog. If they were, I imagine your family and many members of the public would be creeped out or upset.
> but what else do you do here?
Require (or maybe automatically force, if implemented well) those videos to be set to Visiblity: Unlisted. I don't think anyone would be upset with sharing these links with family.