Your children and your first cousin are first cousins, once removed to each other. In casual conversation, most people would probably say, simply, cousin.
Your first cousin's children are your first cousins, once removed. Your second cousin's children are your second 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.
Your parent's first cousin's children are your second cousins. Your children and your second cousin's children are third cousins. Your children and your second cousin - or likewise you and the children of your second cousin - are second cousins, once removed. You and your parent's first cousin are first cousins, once removed.
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 would usually call the children of your husband's first cous by their name. They are not related to you. If you need to refer to them in a general sense, you might call them your husband's first cousins once removed.Yuor husband's first cousin's child is related to you children as a second cousin.
The son of your grandfather's First Cousin is your parent's Second Cousin and your Second Cousin, once removed. The grandson of your grandfather's First Cousin is your parent's Second Cousin, once removed, and your Third Cousin.
Your cousin's sister is also your cousin. Your first cousin's children and you children are second cousins. Your second cousin's children and your children are third cousins. And so forth.
They call you their cousin also!
The English language has not special name for the cousins of your spouse. You could just call them by their first names like you would your friends. If you really like them, you could decide to call them your cousins.
Your children and your first cousin's children are second cousins. Your children and your second cousin's children are third cousins. And so forth.
There is no such thing as great-cousin. There are 1st, 2nd, 3rd, etc cousins and "removed" cousins. The son or daughter of a cousin is your cousin "removed". Example: Your first cousin's children are your first cousins once removed.