Your mother's mother is your grandmother.
your mothers mother is called your grandmother. and your mothers father is called your grandfather.
I call my mother mom
You can call her by her first name or if your comfortable some son-in-laws call them mom.
Mother's: something that belongs to a mother. Example: That's Mother's perfume. Mothers': More than one mother.
If mother is singular: mother's If mother is plural: mothers'
Mothers is more than one mother. Mother's is something that belongs to a mother. "The mothers group is meeting Tuesday." "My mother's car is in the shop."
Your half-sister's mother may be your mother, if you have different fathers. If you have different mothers and your father is married to your half-sister's mother, then you probably should call her "mother." If your half-sister's mother is not connected to your father (i.e. her father married your mother) then there is no relationship name for you to call her mother, other than "my half-sister's mother."
You use mothers for two and not mother's
Mother = äiti. Mum = äiskä, äippä, äityli, äityliini, äite, äitee
The plural is mothers-in-law. (not mother-in-laws)
The possessive form for the plural noun mothers is mothers'.Example: The mothers of several students have formed a mothers' committee.