Can I marry the niece to my parallel cousin's husband?

So a parallel cousin is the child of the father's brother (paternal uncle's child) or of the mother's sister (maternal aunt's child), while a cross cousin is the child of the mother's brother (maternal uncle's child) or of the father's sister (paternal aunt's child).
Parallel and cross cousins - Wikipedia
en.wikipedia.org/wiki/Parallel_and_cross_cousins

I never heard of any such distinction. Why is this important? Lots of people have married first cousins with no detectable effect at all. You are talking about a distant relative.

Nobody uses the term parallel cousin which makes me think there's something fishy going on. The normal term is first cousin and there are only 20 States that legally allow first cousins to marry.

If I read your strange description correctly the husband married into your family therefore any of his relatives are not related to you in any way so there are no laws. They have no blood relationship to you at all virtual strangers as it were.