1. great great grandmother

Question

2. great-great grandmother
3. gret-great-grandmother

[Which one is grammatical?]

Answer 1

#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

Answer 2

1. great great grandmother
2. great-great grandmother
3. great-great-grandmother

Answer 3

Yes -- #3. =)