Terrible parenting 101 in this post. I don't envy you for having to raise, help raise, or in this case "lord over" a teenager...but you sound like a prick.
Your wife sounds like she thought a daddy would fix the girl, and it sounds like you resent the ever living fuck out of her (I'm sorry, "the kid"). Which is truly sad, because I bet that's exactly how your step-daughter feels. "Oh, my step-dad resents me cause I go to private school." Which I'm sure is harder than her old school, not to mention losing her friends, if she was even able to make any with the lords of homework chaining her to a table.
"But it'll be okay cause they wake me up with a fucking air horn"
Jesus tap dancing christ.
Wait a minute, you're whining about her doing homework instead of chores?
This line: Then I explained to her that her job is school and when she doesn't do her work and try to at least make C's that she's screwing up home life for all 3 of us and all 3 of us will be unhappy because of her. I laid this out very nicely and encouraged her to please do her part and help make our home life happy.
I'd like to personally thank you, as a representative for your step-daughter, for giving her a complex. It's not her job to make you happy, it's YOUR job to grow a pair and mold her into a human being. Not say shitty things like this to her. You try to get your wife to eliminate yelling, then you turn right around and bitchslap your step-daughter with passive aggressive comments.
This just in: Teenagers sleep a lot and have a general apathy for everything in life during puberty that doesn't involve the other sex or games/shopping/being a kid. NEWS AT 11.
Also, this fucking private school sounds like total bullshit. Detentions for not doing homework? Get fucked. If that would been the policy when I was in school I'd have to stay late every fucking day.
Did it ever occur to you that maybe you should ask her if she NEEDS to do the homework? Until my senior year, I never did a single page of homework because I didn't need to. I was in general classes with all the other jackoffs, but I would roll in on a test day and get an A without studying or anything. It wasn't until one of my teachers came to me and said "I'm putting you in advanced classes next year, because it's obvious to me that you don't need busywork". Then I got straight A's.