Permanetly deleted photos and videos

As muguy says, you have to believe the warning that appears when we remove pictures from Recently Deleted:

It might be good to show that to your daughter.

If you don't use iCloud Photos, but you have Settings>Apple ID>iCloud Backup turned on, then you may be able to recover data. You should look here:

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support 

“Restore” is what you do when you buy a new phone, so this safety, if you have it set, requires you to erase everything on your phone and replace it with the backup. You would have to get to the backup quickly, usually within a day, before the backup is replaced by a newer one. However, if you did have iCloud Photos enabled, then the iCloud Backup wouldn't make an extra copy.

Perhaps you have shared your pictures with friends-- then you could get them to send copies back to you.

Unfortunately, if you don't keep your own backups to an external drive, then there really isn't any place else to look. To back up your pictures you can just plug in an external drive, select the pictures, and use Share>Save to Files. Alternatively, you can backup to a computer:

Transfer photos and videos from your iPhone or iPad to your Mac or PC

If you haven't done one of those backups, then your remaining pictures continue to be in peril. 

Permanent means permanent. No recovery is possible. You can always recover from the backups that you keep elsewhere and from original sources.