Technically there is no relationship. When introducing her, you would refer to her as My daughter's mother-in-law.
I call her Jane. There is no special name for a person in that relationship.
Your mother-in-law's brother and his children are not related to you.He is your childrens' uncle and his children are first cousins to your children.
The sister of your mother-in-law and her children are not related to you.She is your children's aunt and her children are first cousins to your children.
She is the co-mother in law of you and your daughter's father in law is your co father in law. :-)
I would just call her my second mother
I have most commonly heard a brother-in-law's mother being referred to as a "mother-in-law"
If your brother-in-law is the brother of your wife then his mother is your mother-in-law. If your brother-in-law is the husband of your sister, his mother is not related to you but is your sister's mother-in-law.
Your aunts' mother-in-law.
Daughter
No relation ..
Well my aunt is what I call my mother's brother's wife meaning we're not blood but that's normally how it works in most cases. Or at least with the first wife because my mother's other brother who remarried after his wife passed & I don't call her my aunt.