means that the generations do not line up. First cousins
are two people with one set of grandparents in common (if both are in common, then those two people are siblings). Their parents are siblings. Second cousins
are persons with one set of great-grandparents in common. These are the children of first cousins.
Therefore, once removal is one first cousin and their relationship with another first cousin's child.
A woman's relationship with her uncle is that of niece. The uncle
is either her mother or father's brother, or the husband of her mother or father's sister (there's no such thing as an aunt-in-law or uncle-in-law). The friend is, of course, niece to her uncle. His wife is, of course, her aunt.
FYI, I'm not so sure if it matters how are the first cousins are removed, e. g. whether your wife in the first cousin generation, or the second cousin generation.
The cousin's spouse is also considered to be a cousin (we really don't have good, descriptive words for this in English). Hence his children (and his niece) are another removal.
I believe that these are first cousins twice-removed, but it's tough to say without being able to see an actual family tree.