While it’s true that once something is put online, it’s virtually impossible to eradicate it completely, you can certainly put limits on it once you catch it.
For example, if your child is tagged in a Facebook photo, you can remove that tag. If a photo or video is shared that you’re not happy with, you can respectfully ask the owner to remove it or change its privacy settings.
Although you don’t want personal family photos and videos floating around the Internet, generally they become less findable when stripped of all identifiable information. It’s not so much the multimedia itself which is easy to find, but when it is associated with people, locations and tags.