The English language does not have a widely accepted relationship term for the husband of your first cousin. That person is not considered to be related to you.
If you must describe him other than by name, you might call him your "cousin's husband." Some people use the recently invented term "cousin-in-law."
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AnswerSince they would also be cousins, call them by their first name. AnswerYour children and your first cousin are first cousins, once removed. Your children and your second cousin are second cousins, once removed.
Your children and your grandniece first cousins, once removed, but in conversation they would call each other by their first names.
I would just call her by her name.
Most students never call their first cousins and some don't event know who they are.
If the children of your great uncle's wife are also your great uncle's children, then they are your parent's first cousins, and your first cousins, once removed.If your great uncle's wife has children from a previous marriage, they are not related to you because you have no common ancestor. However, if they were very young when their mother married your great uncle, it may be convenient to treat them like "members of the family" and call them your first cousins, once removed.
Your baby and your cousins are first cousins once removed to each other. You baby and your second cousins are second cousins once removed to each other.
In genealogy terms she would be "spouse of your first cousin."
Your first cousin's children are your first cousins, once removed. Your second cousin's children are your second cousins, once removed. Once you start talking about the children of removed cousins, the possible relationships become more complex. For example the child of your first cousin, once removed is either your first cousin, twice removed (when you are a member of the older generation), or your second cousin (when you are in the younger generation).
You and your father's first cousin are first cousins, once removed.
The children of your first cousin are your first cousins, once removed.
Your father's sister is your aunt. Her children are your first cousins.