1. great great grandmother
2. great-great grandmother
3. gret-great-grandmother
[Which one is grammatical?]
#3 will be correct if you spell "great" correctly! ~~> great-great-grandmother
You can read about the use of hyphens here:
http://grammar.ccc.commnet.edu/grammar/marks/hyphen.htm
1. great great grandmother
2. great-great grandmother
3. great-great-grandmother
Yes -- #3. =)
The correct option is "great-great grandmother."
To determine which sentence is grammatically correct, you need to understand the rules for hyphenation in compound modifiers.
When two or more words work together to modify a noun, they are called compound modifiers. To avoid confusion or misinterpretation, such modifiers are often hyphenated.
In this case, the compound modifier is "great-great." It is used to describe the grandmother, indicating that she is two generations back. To correctly hyphenate this compound modifier, you need to use hyphens between each word.
Therefore, the correct form is "great-great grandmother."