K.G.
God bless you because you are in for a rough time.
I am a step mom also and there are many things that the girls do when they are here that I don't agree with. Their mother is much more lenient than we are.And since you are a step mom, unfortunately you have no rights concerning the children. You can not get information about their health or anything else, that is up to their dad to do.
The best you can do is sit down and have a talk with your husband. you both need to decide what it is you expect of the kids, all of them. It is then important to come to an agreement about discipline and who enforces it. You must absolutely back each other up on all things concerning the kids. Even if at the time you don't agree with the other parent, save it until you are away from the kids before you say anything about it...then talk about it without accusations.
The step children should follow the same rules and be treated the same as the other children in the home. They are all equals, no one is more important than the others. They all should show respect to you, your husband and to each other.
As for her behavior, it seems that she is caught in a bad spot. She needs medicine to help her feel better, and it seems it's not working for her. Dad should step in and go to appointments with her to talk to the doctor about what's going on and what can be done differently.
You and dad need to sit down with all of the children and explain your rules and expectations of them. Also explain the consequences of not obeying the rules.
You and dad need to be a team on this. Be willing to compromise with him and be sure to let him know that you are willing to help him in this matter, as much as you are allowed to do so.
Now, you may not like what I am about to say, and I do understand your frustration, but.....
You need to change your attitude toward this girl. She will pick up on it from you and it will only cause you more issues in the future. She is very impressionable and she will remember how you act toward her later in life. It could also cause a rift between you and your husband.
Now, I am in no way saying you are a bad mom or anything like that so please understand that. I am just saying that if you want her to change and you want your husband to change how he handles her, you will have to set the example.
Remind her of using manners and be sure to thank her for using them. Thank her for good behavior too. I do not believe in rewarding behavior that should be expected anyway, but thanking a child for being good and doing what they are asked is very important. (After all, we expect to be thanked for things too).
Remind her that "When we are in the car we (don't kick, don't scream, etc)". "We go to bed at (this time each night)". Offer to read to her before she goes to sleep, or have her read to you (or dad).
Start a bed time routine with her and the other kids. Let them know what time bedtime is. Tell then 1/2 hour prior to bed that bed time is coming. Have them change into PJs and brush their teeth. Then tell them when it's 10 minuted before bed. Have them say their goodnights and get into bed. Then read with them or turn on some soothing music for them....whatever.
If she has psychological issues, it is important for her to have consistency. You will be surprised how much a difference it will make with her.
Also, be sure to let her know that you love her as well as her dad loves her. She needs to know she has your love as much as the other kids do.
It's tough having step children and not being able to take charge of some situations with them, the best you can do is take charge of what you can and deal with the rest the best you can.
You will have to gently remind dad every once in a while to treat her like he does the other kids, and that he needs to be more tough about behavior that isn't acceptable. But he will catch on to it too. (I've been in this situation so I can understand what you are going through and what you ahve ahead of you).