Your husband's third cousin is just considered your third cousin through marriage.
A third cousin is just that, a third cousin, there is no other name for the relationship.
Your third cousin.
Your grandmother's first cousin's grandson is your third cousin.
Your grandson's third cousin is your first cousin twice removed, and you are hers. You count from the cousin who is closest in generation to the common ancestor in determining what kind of cousin relationship applies.
She is your third cousin.
Cousin in Law
Your great grandmother's first cousin's grandson is your third cousin once removed
Your first cousin's grandson son is your grandson's third cousin. Your second cousin's grandson is your grandson's fourth cousin. Etc., etc.
He would be your son's third cousin.
Your father's first cousin's son is your second cousin. Your father's second cousin's son is your third cousin. If your are asking about your fathers cousins who are in a removed cousin relationship to your father, their relationship to you be more complex, with two different possibilities in each case.
Your second cousin's child is your second cousin, once removed. Your second cousin's child and your child are third cousins to each other.
I believe seeing as it's your father's cousin, that makes them your second cousin. And their kid to answer your question would be your third cousin