Heart,
I think that probably there are a couple of things going on in your relationship with your daughter--and they get all intertwined and mixed up and its hard to untangle them. I think that's where a competent third party could really help. I dont think your husband can do that for you because it might require some tough talking that he cant/wont do. I
dont think your daughter is mature enough to be asked to change her way of perceiving the world. She is a teenager, and some of her "stuff" is recognizably teenager stuff. I have had several and I have lots that work for me and this is so, so typical amongst a lot of them. So, I dont know if that may give you a bit of perspective.
Along those lines, I dont think there is any way your daughter can figure out how to get through this impasse (and I dont mean just the car situation--you two are really struggling on a lot of levels). She just doesnt have the tools, yet, in her emotional toolbox to know what is going on or how to fix it. As an aside, the only tools you may have in YOUR toolbox are the ones that your own mother bequeathed to you during those years of dealing with a traumatized teenaged daughter. To tell you to just look back and ask yourself what you needed in those days, and then provide it to your own daughter is 'way too glib. Ii think a therapist could really help you untangle the different issues that you are both dealing with when you interact.
Your husband is simply not dealing with those issues--he doesnt have them. It sounds like he has boundaries in place (we have explained ourselves, she will be embarassed, its not something I can do anything about, the consequences will be her wake up call). Very healthy thinking, but then he doesnt have to deal with your emotional baggage.
Basically, the only thing you can give your daughter is the tools to navigate life--HER life--the one that started badly, in an orphanage. That created certain emotional liabilities for her that she is going to have to deal with for much of her life. She can do it--her life will look different than some others, but she can do it. She will, ultimately, be the one who has to create that life, that emotional health. You are here to simply give her the tools she needs to do that. She is going to need time as well--time to navigate the normal teenage years that are filled with their own turmoil and time to let her brain grow up (just as any child needs to do--all kids have magical thinking).
Much, much luck to you. CB