Even when I watch Goddess Parvati (an incarnation or form of the Mother Divine), I see that there is so much display of emotions; crying, or asking for forgiveness, etc. Just to make the viewers more engaged, they brought them to the level of common man and common emotions.
The director and producers also want to elongate the episode, that is why they make it a little more dramatic than the actual story. It is not originally so in the Puranas. In the Purana, Goddess Parvati does not go through such varied emotions. It is only in the script that these people have written for the TV serial that you find her and even Lord Ganesha asking repeatedly for forgiveness. What is the need for Him, who is Divinity Himself, to ask for any sort of forgiveness?
See, when you read any Purana, then the Adidaata (the sacred deity on whose life and heroic stories a particular Purana is based) of that Purana is the central character, and the most revered.
For example, if you take the Shiva Purana then Lord Shiva is the greatest, while all other deities and everyone else is subordinate to him.
Similarly, if you take the Ganesha Purana, then Lord Ganesha is the greatest in that Purana.
Again, if you take the Devi Purana then all the other deities, such as Lord Brahma, Lord Vishnu and Mahesh (a name of Lord Shiva) are at the Devi’s feet, signifying her central importance in the Purana. Since all stories in the Devi Purana revolve around her as the central deity, the other deities play secondary roles.
In the Vishnu Purana you will find that there is no deity greater than Lord Vishnu, and every other deity is subordinate to him, since he is the central deity of that Purana.
That is why a deity is called as Isht, meaning the greatest deity, around whom everything else revolves. So, those deities or Gods whom we consider as our Ishtdevta or Isht are the greatest and most revered for us.
There is a very beautiful shloka (verse) by Adi Shankaracharya where he says, 'Mananaatha Shri Jagannatha, Madguru Shri Jagadguru, Madatma Sarvabhutatma, Tasmai Shri Gurave Namaha.'
It means, my Lord (Isht) is the Lord of the entire creation; my Guru is the Guru of the entire creation; and my soul is the soul seated in all living beings.
When a devotee has this feeling, that there is no other like my Lord, then it is called Vishishta bhakti.
When there is this feeling that there is none other like my Lord, then the mind become one-pointed. This is because the nature of the mind is to go towards that which is the most superior.
Now, if you do not find what you have to be the highest, then the mind will start to wander toward that which it finds to be more superior.
So to collect the mind and make it centered deep in devotion, these different stories have been written in the Puranas. That is why in the Shiva Purana, it is said that Lord Shiva is supreme and everyone prays and bows to Lord Shiva. This is the real meaning.
But those who make these TV serials, they have to make it a little more dramatic, otherwise it will be a little boring, and that is why they add some spice to it.
It has never happened that Goddess Durga has inflicted her anger on anyone on Earth. The anger of Goddess Durga is only towards the demon Mahishasura. Even that is not totally in anger, but it is with a certain equanimity and pleasantness. The Goddess simply destroys Mahishasura (symbolic of negativity and inertia) into ashes, by a simple exhalation of her breath, with the sound ‘hummm’.
So these are just different depictions of the mythological stories on TV. There is no need to accept them as the truth.