Hi @Chong •
If you will restore the DC1 from a backup 2 days ago , yes it will replicate automatically and update its information with DC2. Because the backup does not exceed tombstone lifetime.
An authoritative restore is required when you need to restore a specific object from a backup. In this case there is an additional step which involves marking the object to be restored to be replicated from a backup during the domain controllers restoration :
How to perform Authoritative Restore of Active Directory Objects
A nonauthoritative restore , is required when you need to restore a a domain controller from a backup and let it replicate from another healthy domain controller.
Please don't forget to accept helpful answer