She is a white Kishu Inu.
Ginga Densetsu Weed
One day, a traveler decided to adopt the puppies and gave her mate a boar as a trade. The father accepted this, not caring for his puppies. The mother was sad to see her sons leave but also happy as she knew they would have better lives away from their abusive father.
Apparently, she stayed with her violent mate as she was too afraid to leave him. About 5 months after her sons left, she turned ill from stress and died.
See more pictures in Kyōshirō's Mother/Gallery.