Relation name of my mother's sister's son's wife?

My mother has a sister. That sister is then my aunt. My auntie's children are my first cousins. Is that correct? How then do I refer to my cousin's wife and their children. What is the relationship.

The sentence I wish to complete relates to the separation of my cousin and his wife. I wish to pass assurance to the wife and her daughter that they will forever be part of my family. The cousin not so much!

Solution 1:

Your aunt's children are your first cousins. Their children are your first cousins, once removed. Your cousins' spouses are your cousins-in-law or your cousins by marriage. The people I know generally dispense with such technical terms when they talk about their extended family; they just use cousins to describe the various types.

Your relationship to your relations is not governed by familial nomenclature. Notice that

You'll always remain part of my family

contains no terms of kinship.