Parents do have an obligation to their children, so it seems that God would have an obligation to His creation.
The two scenarios do not have the same moral obligations. God is not obliged to anyone. Human beings are under God, and God communicates duties that relate to His perfections and role as King of the Universe.
Parent’s are under the authority of God. Therefore, they do have duties and obligations.
God didn’t have to save anybody. He has no obligation to forgive and show mercy. When God offers forgiveness to us, He goes above and beyond.