backup and migrate Cannot delete or update a parent row: a foreign key constraint fails
Backup and Migrate module may not be compatible with CiviCRM, and may not understand how to handle the many foreign key constraints within CiviCRM.

Here is the easy way:


Drop the database entirely (back it up first please)
recreate that database with the same name
then restore from your backup.


Here is the hard way:
Particularly, if a failed update has altered the table structure of your database, simply restoring may not work with any tool, because the schema has changed. More information:
http://wiki.civicrm.org/confluence/display/CRMDOC/Ensuring+Schema+Integrity+on+Upgrades