This kid has been poisoned by PAS, added to that she's probably a chip off the old block with BM? I agree, never be alone with her! Also watch the baby too!
SD, 15 at the time, here did not get her own way with DH and he put her on a time out outside the french doors at the back...out the front she called the cops and said we'd put her out! Anyhow, this occasion, she kicked until DH thought the glass was being broken and he went out to tell her behave. She beat herself up, called the cops and told them her daddy had done that to her. The ONE cop who had never arrested her (juvenile record is inches thick on SD) was on duty and he actually believed her, cuffed DH and took him away! After that I refused to be alone with the girl and stood outside with one of our neighbors waiting for SD's older sister to arrive and take her because there's no way in hell was I going to be taken to jail over the head of a psycho kid! 72 hours DH was held because of a burned out tail light almost a decade ago that was not dealt with in another county.
You can only look forward to similar if your DH does not step up to the plate. Some kids are just BAD, sociopaths with no concience whatsoever. Even if DH does step up to the plate you really do have to do some deep thinking and get strategies in place to deal with your SD. DH does have a point with the respect thing, he's not the only one allowing that crap...you are allowing it too in the sense that you do not speak up for your own self and expect DH to stand for you. Polite and firm is hard to do when a kid manipulates and rattles nerves. I located EVERY button that SD here could push, mentally switched them all off and it was a very quick change in her behavior towards me. She saw it as a game and as soon as I 'stopped playing' then I was no fun any more...it's really that simple! I was going through similar stuff to yours, I was exhausted with it all and I had just had enough, kind of like where you are at now? I wish you luck!

SD MADE dh get your hairbrush from you while you were using it. NO she didn't, she may have asked him to, she may have screamed, yelled and cried saying that she wanted it, but he is a grown man and he could have said "Wait a minute till my wife is finished with it" or use another brush, comb whatever, he was not forced by a child to take your brush, it was easier on him to take your brush from you and give it to her because it shut her up. Your biggest problem is DH.

Should he speak to her again - Hell do you even need to ask that question. Both you and DH need to work out what the rules in your house will be, and SD will follow those rules, it will simply be a case of YOUR HOUSE your rules, and BM's House - BM's rules. SD will get used to it if your DH remains consistant, seems to me your DH is not being consistent. After all, he was the one who got the hairbrush and he should have told her to get out the shower as others were waiting and if she didn't he could have turned off the hot water it's easy enough done.

If you are afraid he won't believe you about the conversation she had with your mother, have your mother and SD present when you tell him. Calling SD out in front of DH and your mother may just teach SD a lesson.

You may want to point out to DH that if this child keeps lying sooner or later you and DH will be getting a visit from child services, and they won't just be looking at taking her away, they will be looking at this new baby brother as well. Do you not realise this.

Hah ha ha I did exactly that with my step-daughter. But you don't turn the water off like the guy said above that would be too obvious. You turn the gas off. This gives the kid 40 gallons of hot water about 1/2 of what they'll use being the selfish brats they are.

It's a scream. About half way through the shower the water suddenly gets colder and colder and there is nothing to be done but rinse out ones hair while cold water cascades around her body and she quickly gets out. If nobody sees you turn off the gas nobody will even know what's up.

Look at the the water heater down low. Usually its a round plastic dial and often red in color. Its about 2 inches across the diameter, from one side to the other. It turns either direction. It has a setting called "PILOT" which simply means its on but the water will not be heated. Kinds like the radio is on but the sound is turned so low you can't hear anything.

First note exactly where the knob is now. You'll want to return it there after she's out of the shower. Then turn it to pilot. Be careful not to turn it to "off" or it really be off. Then return it to the original setting after she turns off the water in the shower.