You could be 7th cousins 6 times removed or 9th cousins 4 times removed.
Your first cousin's daughter is first cousin once removed to your grandson, and he to her. Your second cousin's daughter is second cousin once removed to your grandson, and he to her.
There is no relationship in the English language that is called a "half cousin." Everyone who is your cousin is related to you through one and only one parent, so, unlike a "half brother" there can be no such thing as a "half cousin." If you have a first cousin (child of your aunt or uncle), then your child and that first cousin are first cousins once removed. If you have a second cousin, they your child and that second cousin are second cousins once removed.
Your sons children and your daughters children are First cousins. The idea is that First cousins share a grandparent, second cousins share a great-grandparent, third cousins share a great-great-grandparent, and so on. The degree of cousin relationship i.e. "first," "second," etc. is used to denote the number of generations between two cousins and their nearest common ancestor. Now, a term "removed" is used to refer to the number of generations separating the cousins themselves. So your first cousin once removed is the child (or parent) of your first cousin. Your second cousin once removed is the child (or parent) of your second cousin. And your first cousin twice removed is the grandchild (or grandparent) of your first cousin. etc. Thus in this case they are first cousins once removed.
Your niece and one of your grandson's parents are first cousins. That makes your niece a first cousin once removed of your grandson.
Your child and your first cousin's child are second cousins. A full generation is another set of cousins. For example, the second cousins' children will be third cousins, etc. Now here is the tricky part. You are a first cousin once removed to your cousin's child and your cousin is a first cousin once removed from your child.
Your grandfather's cousin is your cousin twice removed. Her husband has no direct relationship to you.
Your grandmother is first cousins with cousin. Your parent would be the second cousin of the cousin's son. That would make you second cousins once removed.
Your cousins child is your first cousin once removed.
Your grandson and your first cousin are first cousins, twice removed. Your grandson and your second cousin are second cousins, twice removed. and so forth.
If you are first cousins, they would be a first cousin once removed.
You are first cousins once removed.
Your daughter is first cousin once removed to your cousin. Your daughter is second cousin to your cousin's children. Your cousin's children are first cousins once removed to you
Your first cousin's grandchildren are your first cousins, twice removed. Your second cousin's grandchildren are your second cousins, twice removed. And so forth.
Your cousin's daughter is your first cousin once removed. Your daughter and your cousin's daughter would be second cousins.
Your cousin's child is your "first cousin once removed". If you were to have children, your child and your cousin's child would be second cousins. The son of your cousin's son would be your first cousin twice removed. Look at it like this: you * your cousin * ** your cousin's son (your cousin once removed) ** *** your cousin's grandson (your cousin twice removed)
The relationship between your sister's (or brother's) child and your cousin is the same as the relationship between your child and your cousin. Your child and your first cousin are first cousins, once removed. Your child and your second cousin are second cousins, once removed, and so forth.
You and your first cousin's son are first cousins, once removed.