single word requests - Is there a special English name for one’s mother’s sister’s son?

Cousin is the standard term in American English for the descendants of your parent's sibling. The child of your parent's sibling is your first cousin. The grandchild of your parent's sibling is your first cousin once removed.

To indicate that the cousin is related through your mother, you can use the term maternal cousin.

While I have never heard the term used, you could indicate that the maternal relationship is through her sister by adding sororal, as in maternal sororal cousin.

In English, we do not have a gender specific reference for cousin (in contrast the the French cousin/cousine. You could add male as in maternal sororal male cousin.

Obviously this is not a single word descriptor.

This relationship does not seem to be listed in the quoted law, but that is a legal question rather than a language issue.