Technically it is a violation to give away hosting to a third party from your free hosting account, which would include family members. Is there any reason why you don't help the kids set up their own accounts instead of using yours?
That being said, the ToS also limits galleries to a max of 500 mb for images/videos, which may be something to keep in mind seeing as there's a gallery on site.
Most of the space on your account is taken up by photos which appear to belong to a personal gallery, including having a backup double of all images. I'd start with cleaning up that part first.