how to reset my 2012 mini mac back to how it came from shop after ive backed it up to my daughters time machine it wont let me sighn in now

Hi, I never use TM myself, but since nody else has answered so far...'

Bootup holding CMD+r, or the Option/alt key to boot from the Restore partition & use Disk Utility from there to Repair the Disk, then Repair Permissions.

If that doesn't help Reinstall the OS.

Reset Password 10.7, 10.8...

http://reviews.cnet.com/8301-13727_7-20087723-263/how-to-run-the-password-reset- utility-in-os-x-10.7-lion/

Then Reset your Keychain...

http://support.apple.com/kb/TS1544

AS far as TM...

Have you looked through Pondini's extensive TM help site?

http://Pondini.org/TM/FAQ.html

http://pondini.org/TM/Troubleshooting.html

Can't imagine something not being covered there.

1. Temporarily turn off Time Macnine on your daughter's compter.
2. Attach to your daughter's Time Machine drive
3. Launch Time Machine on your computer and select her Time Machine drive to hold your TM backup. This will not overwrite her backup it will create a sparse image bundle to contain your backups.
4. After the Time Machine backup completes, it may take a long time so be patient.
5. Reboot your mini while holding down Command+R to boot from the recovery drive. (If there is a problem with your recovery drive you can boot holding down Command+Option+R and that will boot your system from an internet recovery drive on Apple's servers.)
6. From the recovery drive run Disk Utility and erase the hard drive on your mini.
7. reinstall OS X from the Recovery drive, this will require a high speed internet connection.
8. After OS X is reinstalled it will reboot and begin the system initialization process. Very early in that process it will ask fi you want to restore from another drive or from a Time Machine backup.
9. Choose the Tima Machine backup and the Migration Assistant process will be initiated.
10. Choose the image of your computer on your daughter's Time Machine drive and the rest is up to Migration Assistant. The restore process may take a long time to complete so be patient.
11. When your system has been restored on your mini be sure to turn Time Machine off unless you have a drive you want to use every hour.
12. Be sure and turn Time Machine back on on your daughter's machine.