Set up Wrong Phone

The way to delete everything from your wifes new iPhone and start from scratch is by going to Settings > General > Reset > Erase all Content and Settings. Her new iPhone will then restart and you can set it up again. (Before you do that, you can log out of iCloud on the new iPhone in Settings > iCloud to disable Find my iPhone - otherwise it will ask for your Apple ID password during setup.)

If I understand correctly, your wife does not yet have an iCloud account and her old iPhone does not have iCloud configured so far? Then the next steps are:

• Let her create an iCloud account and log into it on her old iPhone
• Enable iCloud Backup on her old iPhone and perform a backup
• During setup of the new iPhone, specify her newly created iCloud account and restore from the backup

Finally you can enable Family Sharing if you wish:

Set up Family Sharing - Apple Support

See this article for details about restrictions / parental controls:

Use Restrictions on your iPhone, iPad, and iPod touch - Apple Support

What do you mean by "I set up the wrong phone"? Did you choose to restore it from an iCloud backup and chose the wrong backup?