It really sounds to me like you're making the mistake of doing the same thing repeatedly, expecting different results.
A LOT of people go through moody apathy during the early to mid teen age years. I know I did. I even dropped out of school. 5 years later got a GED, tried college for a semester or two, wasn't feeling it, dropped out of that. Worked at a liquor store for half a decade, got married, had kids, took care of my mother for a few years until she passed away, it wasn't till I was 28/29 before I went back to school. Kids are 7 and 9 years old and shit and I'm retaking basic high school algebra and trigonometry courses and whatnot. But you know what? I chose to do it in my own time and because I got the leeway to do that, I'm doing very well, I'm passionate about my education and my kids aren't hypernegative to school and learning either.
Sometimes it take time. I see you say in the first post that "We tell her we can't support her forever". That may be. But she's 14. Not 18, not 20. Not 24. Not 30. Not 40. You're talking to her as if she's like 24 and living in your basement pissing in bottles. You should take into account the fact that as people's life expectancy increases, the age at which mental development is fully achieved will be more and more delayed. 14 years old is like one of the moodiest points, awkward too, especially for girls. Try to see the world from her point of view, her perspective, I really get the vibe from the original post that you haven't done this, like at all. Its super necessary, I think.
I mean at some point you have to realize things have gotten out of control. That point, for me, would be when the wife is floating the idea of using an air horn to get my kid out of bed on Saturday morning. Let her sleep in. When I was a kid I never slept in (lol adhd up at 5 am). But almost all my friends did. They regularly slept till 10 and 11 on weekends and summer days. No one ever thought it was abnormal. Some kids actually physically REQUIRE more sleep during the teen age years to accomodate their physical and mental/emotional growth, since most growth and repair mechanisms of the body are conducted during resting phases.
Just because a kid is having problems today, or going through a period of difficulty, doesn't mean you should be brow beating them and berating them and trying to force them out of it. And it doesn't mean they won't figure things out by 18 or 20 or so. You're making things worse. This may sound crazy but try....just leaving her alone. Forget the chores. Who cares? Its fucking trash or dishes. Is it really worth all the fighting? Family is supposed to be about unconditional love and support. Try being her father, and her friend, not her authority figure all the time. Most of the time I can GUARANTEE YOU when you are lecturing/talking to her she's thinking "I don't have to listen to you, you're not even my real dad". I was adopted at 6 months old and I pulled that shit on my mom and dad in my teens CONSTANTLY anyway during arguments, because I knew it hurt their feelings.
I have two kids. 11 year old daughter going on 12 and a son who will be 9 on Christmas eve. I cut their umbilical cords myself when they were born. I know I would never tell them something like "I can't support you forever" because its not true. I would do anything in my power to assist my childen financially, or in any other way necessary, even if I was 80 and they were 60. That's what family is. My father and mother went out of their way to help me, my wife, our children, and my sister, her husband and their children, multiple times over the past decade since we became "adults" when times were hard. Like through 2008/2009 at the height of the economic collapse while my parents 401k was being massacred and my sister and her husband and their 4 kids all moved into my parent's house for over a year because my brother in law had lost his job and they had to move back here from Alabama.
Maybe I"m old fashioned because, despite being adopted, my family has, until the past 4-5 years where its been whittled down by age and death, been very solid. Few divorces, little to no single parents (none whatsoever of either in my immediate family, both sets of grandparents were married for over 50 years before they passed and my mother and father were together for 40 plus years before my mom died this past march) but the idea of abandoning my kid is anathema to me, personally. Family is all you've got in this world, when it comes down to it, and family isn't always defined exclusively by blood.
I know that if my parents had said that they weren't going to help me and stand by me while I figured out how to be an adult, I'd be about a 1000x more dysfunctional than I am now, and yes it took me a long time to go back to school after dropping out in my teens, but I just achieved an associates in the sciences with a 3.8 GPA and am pursuing two degrees with three majors (chem/bio/ant) and a minor (mandarin) now with probably two and a half/three more years to go to finish it (140 credit hours required for a triple major blah).
You really need to decide: Are you the girl's father, or her step father? Do you love her? Or do you see her as an obstacle to your happiness. If she's an obstacle, you probably shouldn't even be in that home. Get out of the way and let mom find a dad who will care, cause you're not helping. If you're her father, then you accept her for who she is. You love and support her and you want to talk to her and help her any way you can but you do not want to brow beat her into submission and into becoming the person you want her to be. That's not love. Someone in your life might have told you that's love, but they were wrong.
I know if I was 14 and my real dad barely had any hand in raising me and my step father was a domineering authority figure to me, I"d take a lot of long showers and sleep in on weekends as well, and probably raise hell at school, just because. Its a vicious circle. She does something wrong, you yell at her, she becomes more rebellious and apathetic, causing more havoc, causing you to respond; wash rinse repeat as unnecessary. You're creating the type of rut here which will destroy her, all because you can't just leave her be. In a way, she's striving for negative attention, and you're giving it to her. Stop giving it to her, and give her the leeway to define her own existence for awhile, see if you all can't come out of the experience with a bit more respect for one another's point of view at the end of all this. Remember, family is a multiple path intersection, not a one way street.
Parenting is a thankless job. If you had to fill out paperwork to become a parent, one of the first paragraphs you would have to annotate is the one stipulating that parenting is thankless, that your kids may never once in their lives come to appreciate you for what you've done for them, and if they do it'll be when they're parents in their mid 30s or 40s and you're on your deathbed. You have to just go ahead and accept that right now if you're going to be a dad to anyone.