Ugh, Teenagers

I have mentioned my niece, Laura, recently. She's in Ohio, I'm here. We email each other a fair bit. She's a very tempestuous 14. She is very clingy and needy and will somewhat often throw temper tantrums even through email, and from my adult perspective for no good reason:
She doesn't want to share me with her sisters or other family members
She wants me to read her a bedtime story
She bewails bedtime.
Something-something, security blanket.
Sometimes it's OMG, she just has to come live with me
I have to come home to Ohio

I get less grief from the 18 month old some days, I swear to jeebus. And I know what she wants. Attention. And she is choosing an unhealthy way to get it.
A lot of the time, I just don't respond to the email where she flips her lid. I will occasionally explain how that's not acceptable, and yet, I haven't really seen a marked difference. I'm at a serious disadvantage. I rarely talk to her on the phone, I do not have a chance to see her face to face. But this must end. How do I guide her towards more mature behavior without threatening to abandon her?
Help?