I agree with taking your daughter for a full evaluation at the best pediatric psychiatric hospital available. My stepson has been, as you describe, all of his life and at the age of 10 currently continues to have a lot of problems, is emotionally explosive and has threatened suicide and to harm others. He was never fully evaluated or received the appropriate treatment he needed. I have been his stepmother for about three years now, and am just now getting my husband to realize the necessity of having him fully evaluated.
As a step-mother I can understand what your husband is going through, so I will offer my sympathies to him. I can understand why he is frustrated. I imagine he entered his marriage with you in hopes that he could help your daughter. I also imagine that over time, your daughter's behavior has overwhelmed him and his frustrations have grown to the point where he is easily set off. I have walked in his shoes and know how he feels. There are many times when I do not "like" the behaviors of my stepson. There are times when he pushes me past my limits, and I do not want to be around him. He actively rejects me on a daily basis, and I do not have that motherly bond with him. However, don't get me wrong, even though I do not "like" the way he acts, I care very much about my stepson and his future, and in that regard I try to focus on the things that will strengthen our relationship and try to avoid the things that damage it. It's not perfect by any stretch of the imagination, but we are working on it.
In order to reduce my stress level, I have had to step back and insist my husband parent his children. He wanted me to take care of everything, so that he didn't have to do anything but go to work, come home and relax. He's just that way. However, children by nature will be more responsive to their parents than an outsider. They will understand and forgive punishments from their parents, but the same is not true for an outsider. Trust me when I tell you, my stepsons see me as an outsider and may always see me that way. My stepson is angry with me because I have taken his mother's place, changed the rules and set boundaries. I am much stricter than his mother ever was. His life is not the same as when his mother was alive. This whole process brought me more stress then I bargained for to the point where it started to affect my marriage, and I started looking for a way out...but that's not what I really want in the long run, so changes needed to be made.
When my husband is home, he is responsible for everything when it comes to his boys. I prepare meals, and participate in fun activities, but I try not to parent his boys when he is at home. I do not supervise them in their chores, and I do not participate in the going to bed ritual because there is usually a lot of fighting and arguing, which I do not tolerate well. The less parenting I do, the better. If I need the boys to do something, I tell my husband in private and then he tells them what needs to be done. I stay at home so the boys don’t have to go to daycare, and also so I can help them with their homework. Even when they are with me and their dad is at work, if there is a problem, I call their dad, and he talks with them to help sort out the issue or sets whatever punishment needs to be set. It has taken a little time, but it has helped. I don’t feel as stressed, and the boys now see their father more as the disciplinarian, instead of me.
This all has taken a long time to put together. We have had constant conversations in private about how things should be approached and what should be done. We discuss what to do before things happen, and we discuss what happened afterward and how we could have done things better. We have even gone to a couple of family therapy sessions, which have been helpful, especially in areas where we disagree. All of this has helped us become a united front, which is absolutely essential.
I hope some of this helps guide you in a positive direction. Marriage is hard and blending a family makes it even harder. If making your marriage work is important to you, you will need to seek outside support to help your family through all the problems you are facing.
Blessing and hugs to you all.