Hi Inder, I have a 13 and a half year old daughter too, in the 8th grade.
I'm not exactly sure how it happened, but she and I have become something of a management team in the business of her life.
Make no mistake, there IS a line, and I AM in charge.
But I've noticed there are SO very many bonding opportunities everywhere, that often start out as potential conflicts.
For example, if there is something she does not feel like doing, putting her laundry in the hamper (putting those freakin' straighteners in the cabinet uder the sink!)brining her dirty dishes down, cleaning up a mess she made (MAN can she spread out!) and she blows me off a little or stalls, I will hover, I will say something with humor, I know I get lazy too sometimes, here's what I do to make the task better, faster, easier, etc...definately sucks, but it's gotta be done, right?, I ask her. I wiil pick up a folder and motion to her backpack, generally she will sigh and just get busy.
There, now we are together, collectively disliking a certain task, but understanding it's just got to be done anyway. I will not do it for her, but I AM on her side.
I do not sweat the small stuff. I let her have her hair the way she likes (although she knows I DON'T like it. She's an excellent student, which is a constant subject of conversation, in the manner of praise of couse, but I ask VERY specific questions about her day, classes, assignments, consistently. I let her vent, whine, complain a little about most things, I say, I KNOW JUST what you mean! And then tell something that happened to me. I think she has a lot of self respect fueled at least in part just by my showing non-threatening interest in her life consistently.
She is a normal modern american teenager, always texting, on the laptop, too many friends, even a boyfriend, a whirlwind of emotions and opinions, which change from conversation to conversation.
I am NOT crazy about the boyfriend thing, but that too has become a bonding opportunity. We have had very serious conversations about the choices she makes will have to make...but mostly we giggle together about how DUMB boys can be!
I DO piss her off from time to time, and this is her thing. She gets a SHOCKED look on her face, throws her arms up, stomps loudly up the stairs, and slams her bedroom door (on the rare occasion I have to say NO, not because she's spoiled, just because she really doesn't ask for much!). A little time goes by, and honestly just when I'm about to go up and talk to her about it, maybe elaborate as to why I said no, she will come skipping down her normal jolly self and the thing is never mentioned again. I see no point in reprimanding her for stomping away/slamming the door.
Try to look for ways to keep your daughter close. Engage her in conversation, doesn't matter what about. Ask her everyday, who did you sit next to at lunch? Did you have gym? What did that english teacher wear today?! Something anything specific so she knows you are into her. If she answers snotty, just drop it. Ask her something else later. Brag about her on the phone, to neighbors, so on.
Anyway, sorry so long, I'm just rambling. Lastly I agree with a lot of other posters, phases come and go, she WILL get nice again!! Good Luck and enjoy her!