On your family site click on the ‘Photos’ tab and then click ‘Albums’ on the left to open the list of the photo albums you currently have on your site.
Click on the album you would like to delete, and then click on the icon next to the album’s title.
Select ‘Delete album’.
Please note, the media items in the album still won't be deleted and will remain in your family site's Photos library.
In order to delete them, follow the instructions described here: How do I delete a photo from an online album?