Names of family members are capitalized Mother Father except when accompanied by a?

You are correct! Family member names are capitalized (Mother, Father, Aunt, Uncle, etc.) except when they are accompanied by a possessive adjective.

Here are some examples:

Capitalized:

* My Mother is a great cook.

* I went to visit my Uncle John.

Not capitalized:

* My mother's birthday is next month.

* I went to my uncle's house.

This is because when you use the possessive adjective ("my", "your", "his", "her", etc.) it already indicates that you are talking about a specific person.