for the suggestion on outing... i think the 2 of us pretty much
don't have a common topic of interest and i expect her to give me
short answers to my questions, if conversation does not work. i'm
afraid she'll alienate me even more when she becomes irritated by
my questions..
and i can't get her grandma to move... it's too inconvenient for
her 
Hmmm.....i think you need some practice and certainly need
to do homework on getting her "trust" before you
can proceed.......start gathering information of what you know
about your daughter?
Determind the moment to talk to her when both of you are in syn.
Eventually you have to find the right moment.........you know it
when it happen.
Take a few moment each Day and Visualized those "right moments"
and visualized those "Happy" activities that "both" can
do together.
i think some preparation such as
1) reflecting what you were like when you were her age?
How do you speak at that age and what was actual intend?
2) list down what you think she likes vs what you enjoy.
3) Do you know her friends at school? (Do you notice your
daughter don't have friends at school?)
4) when is her birthday do you ever give her a "birthday
Bash" invite her friends small group? Teen
birthday party and kids birthday are different. (that is
the easyest thing to do to be part of her life!
organized birthday )
5) Did you know by building relationship between you and
her; help your daughter to learn how to
make friends in school.
5) Activities helps to break the ice. you probably need to work
on "Trust" from her. You must have hurt her at some point that you
didn't even realized.
6) Friends don't judge but have fun together.....and can
relate.
If you can't relate now....how do you proceed to the next
topics.......
7)she is a girl....eventual "girls talk" share with her
your first crush..."she will be shock" who is
mom!!!........what i am trying to say is you have to break down
first before she does. bring your level down let her see
you were once like her..... Tell her is perfectly normal to be
interested in boys....the do's and don'ts
You certainly do not want her to learn flowers and bees
from friends and internet.....So this "Friends thing is more
important for you as a parent.....You want her to come to you in
confident when she has questions on bees and flowers.
What is not
1) you sit in your room and tell your daughter you wanna be
friends.......she is going to give you the strange Look.......and
stay far away.
2) don't asked question......if she don't like so long as you
know she isn't going to Take drugs or get pregnant.
3) Don't use her information to judge her. she
will stay away you for a long time.....
All these takes time.....Good luck.