Good afternoon and welcome to JA.
First and foremost - it will be essential for you and your husband to agree upon whatever discipline you decide to implement with your daughter (step-daughter). If there is any disagreement between you, your daughter will use this to her advantage to "split" you (not in terms of getting a divorce, but sneaking around with the least restrictive parent to get things she wants.)
I agree and have seen this happen
While it is inappropriate to diagnose 3rd party over the internet, the problems you describe are far more pronounced than typical "teenage acting out."
she will also go to her mother and get permission to do something that she wants
I also agree this is not normal "teenage acting out"
There may be reason to believe there is some significant psychological/psychiatric impairment warranting intervention by professional(s).
This being the case, I would urge you to talk with your husband about considering a formal psychological/psychiatric assessment.
we are trying to locate a psychologist now
You may want to check your insurance to see who is covered and then narrow down to somebody who specializes (if possible) in adolescents. You may also want to consider a specialist who deals with substance abuse.
In the event you experience another "crisis point," it may be worth either calling and ambulance or taking her yourself to the ER for an evaluation and possible immediate treatment (which might include a brief stay in inpatient).
In the meanwhile, you and your husband (and any other children) would likely benefit from some family therapy to help bolster your relationships while the "tornado" is loose in the living room. It will also set the stage to let the family know, "Yes, mom and dad are aware of the problem, and we're working to find a solution, as the parents who are in charge here."
To answer your question directly about discipline, I believe your problems (as you described them at least) go far beyond the question of "simple discipline." I think your daughter is trying to communicate to you that she is out of control and, likely, in a considerable amount of pain/fear/hopelessness.
By no means has your daughter earned privileges to drive a car (her's or anyone's)... and this needs to be spelled out NOW if there is any misconception that she'll get to add an auto to her arsenal of misbehavior.
So, I would urge you to consider the next steps as being: a thorough psychological/psychiatric evaluation and the implementation of therapy/treatment as soon as possible. These behaviors are serious and potentially dangerous to herself and others.
Because you are both still the parents and she is still a minor, she does have to consent to participate... you just have the challenge of getting her there. :)