Is this form of mother mentioned in any scripture?
Shanta Durga form of the mother is mentioned in Sahyadri Khanda of the Skanda Purana. Its English translation is unavailable.
इति श्रीस्कादे उत्तररहस्ये सल्यादिखण्डे नागाव्दयमाहाःम्ये
सूतशौनकसंवादे शान्तादुर्गाप्रादुभौवो नाम दहिनीयोऽ ध्यायः
So, the above title contains the name Shanta Durga. And the chapters contain the total story in which Durga manifested as Shanta Durga.
Wikipedia mentions it with a citation (As the scripture is completely in Sanskrit, I am quoting the gist from Wikipedia)
The second chapter of the Sanskrit Nāgavya Mahātmya, Śāntādurgā
prādurbhāvaḥ, is a part of Sahyādrikhaṇḍa which is the chapter of
Skanda Purana gives detail about this. Only the title of the
chapter mentions the goddess Shantadurga and no where else is this
epithet of the goddess mentioned. This section refers to a certain
sage Śāntāmuni, a resident of Nagavya (modern Nagoa). The goddess
appeared before Shantamuni and hence she's known as Shantadurga.
If yes what is her origin and other details.
Shanta Durga is also called Santeri. As we have already seen one of her manifestations in Skanda Purana. The following is mentioned by the temple website about another manifestation of Durga in the form of Shantadurga
Shree Shantadurga is one of the forms of Goddess Adimaya Durga. It is
believed that once there was a fierce war between Lord Shiva and Lord
Vishnu due to which the entire world was distressed. Hence Lord
Bramhadeva prayed and beseeched Goddess Adimaya Durga to intervene and
stop the war. The Goddess held Lord Shiva by one hand and Lord Vishnu
by the other hand and brought about reconciliation among them. This
stopped the war and brought peace to the world. This form of the
Goddess Adimaya Durga, is known as Shree Shantadurga.
This story seems to be present in the Marathi book named Koṅkaṇa Mahātmya as per some sources 1 including Wikipedia and the book is unavailable online.
(The video source explicitly says that Koṅkaṇa Mahātmya contains the whole episode of the manifestation of Shantadurga mentioned by the temple website.)