Stepmom stuff with a defiant pre teen? Please help

I have a 12 yr old stepdaughter that would argue with a boot.  She doesn't listen to me at all.  It's not like she does things I don't want her to do later, she'll flat out tell me no I don't have to listen to you.  She lies and when you catch her in a lie, she'll stick to her lie. Yesterday she was kicked out of class for arguing with a student over the fact that she was being rude to a different student.  Last year at the end of the year, a girl punched her for, in her words, "being rude."  I know that student shouldn't have punched her, but she is very rude and will argue with you till no end. 

I make her sit outside when she tries and argues with me, which is not fun, it's very hot outside.  Today she told me she wants me to "drop dead" she also said that she hates me because her dad loves me, and that I will fall off my throne.   The sitting outside part is her dad's idea, and I think it's all wrong.  I told her today that her dad may eat her crap, but the rest of the world isn't going to, including me. 

I am 27 years old and my only bio child is 4.  Somedays I feel like I'd be better off just me and my baby.

I know what gets her, using the computer, and she has her own, but she will butter up to her dad and she'll get her way within days.  Not to mention she got into that trouble yesterday, and her dad let her spend all her free time on the computer still.  When I mentioned it to him, he didn't do much but get mad at me. 

I just don't think all of this is worth being with their dad sometimes.  I love him, and it's a long story but I am part of the reason that he has custody of his kids today.

I really try not to fuel the fire by talking to her at all, but sometimes she will say the worst things about me.  I do try an make sure she has her facts right.  I got so mad about an hour ago I still haven't calmed down.  I swear I thought I was going to have a heart attack.