She is your aunt. This is true in most traditions. English does not distinguish between an aunt by marriage (father's brother's wife) or an aunt by blood relation (father's sister).
your father-in-law's house
Your parent's brothers are your uncles and your parent's sisters are your aunts.
Your father's brother's son is your first cousin. The English language does not have a name for the wife of a cousin. You would simply refer to her as "my cousin's wife."
granddaughter
Your half-brother...
I think you mean 'Otosan'. This means 'Dad' or 'Father'. I get the impression from my study that wifes sometimes call their husband 'Otosan'.
Mother in-law
thats her brothers wifes brother.....
You're wife's brother's wife is your sister-in-law.
Sugar Daddy
If she is now married to your shared father, she is your step-mother. Otherwise she does not have a direct relationship to you.
Your father's brother's child is your cousin. A first cousin is anyone who shares one or more common grandparents with you.