Your half-brother's daughter is your niece. Your niece and your son are first cousins to each other.
your uncles daughter would be your cousin
you would be her aunt and she would be your niece
Since your uncle's sister is your aunt, her daughter would be your cousin, just as your uncle's daughter would be.
It would be a second cousin.
She would be your 2nd cousin.
Your brother's daughter is your niece. Her daughter would be your great-niece. You would be either her great uncle or great aunt.
The relation of the mother;s sister to daughter is niece-aunts.
That would be second cousin once removed. Your parent and your grandmother's sisters daughter were first cousins. You and the daughter's daughter are second cousins. There is a difference on one generation between the two of you.
Being your sister's brother or sister you would be an uncle or an aunt to her daughter.
I think the kids would be second cousins
If she's not your mother, that would make her your Aunt.
You are one generation out of synch. That would make you first cousins once removed.