Dear H.,
Step-parenting is hard enough ... stepmother to an adolescent girl is the worst! I've been there twice, unsuccessfully, and I understand. So I have no magic, just a bit of direction and some questions you need to ask yourself.
1) Get counseling ASAP. Find a therapist who has training and experience in stepfamily issues. (That doesn't guarantee they'll be great, however. And if you don't "click" with one therapist, remember, you're always free to try another.) You'll probably need individual, couples, and family counseling. If your husband won't go, go by yourself. And ask yourself if you need to be with someone who won't work on making things better.
2) Work on your own base of power. Do you need to stay at home for a twelve-year-old? Could you find a job instead? Sounds like your stepdaughter doesn't appreciate having you home. And at 12, she's old enough to be on her own for a couple hours. If you get a job, you'll be with other adults, and treated like one (we hope!) Best of all, you'll have money, which equals independence. Save it! Right now, you may feel trapped. You need the feeling of knowing you can leave -- for a few days, or for good.
3) For now, get out of the equation. You can't possibly win in your dealings with the daughter, so is it possible to temporarily withdraw? e.i., have her father decide her responsibilities and also be the one who checks up on them? (For example, loading the dishwasher ... if she doesn't, and he doesn't catch it, don't nag her and mention it to him. So there aren't enough clean dishes? Eat pizza on paper plates.)
You may feel as if you're giving up your responsibilities or control, but it sounds as if you've already lost this. You've become the "bad guy", the one they can blame for everything. Why not step away from a conflict you can never win?
Honestly, if it were me, I'd consider going away BY MYSELF on a nice vacation for at least a week ... to a spa if money permitted, or else to visit a family member. You need the break, and it might do your your husband and stepdaughter some good to see how tough life is without you. They may find they need you, and thus be more willing to work things out.
For some quick help, I'm sure there are lots of books and internet sites out there. I believe there's an American Stepfamily Association. But nothing can work until a few basic ground rules are in place between you and your husband.
-- NO LYING. You have to be able trust him. And if he won't take your word over his daughter's ... why would you stay? Your daughter's lying will also have to be dealt with -- by him -- so it stops being profitable.
-- You and your husband are a team. You have to both be dedicated to making the marriage work. And of course, you have to have a united front when it comes to his daughter. If she can keep splitting you apart ... well, she wins.
As I'm sure you've realized, there are no short-term fixes for your problem. And it is an agonizing one! Please keep us posted. And if you want to contact me, I'm always here to listen.
W.