Acknowledge the challenge.
You knew that your spouse was bringing a child from a previous relationship into the marriage, so that part of your situation can't be a shock. If you're shocked about having to come up with a plan to resolve difficulties, get over it! Nobody said this would be an easy hill to climb. You need to sit down with your spouse to discuss money, discipline, childcare and any other issues that you haven't mutually agreed upon yet.
Have your discussions outside of crisis.
If most of your discussions are taking place within the context of an argument, you need to stop. Agree to make time to talk calmly and rationally. This is important for you but more important for your children. When you argue in front of children you change who they are. For you, the fight is over when it's over. For your children, it doesn't end. They don't see you make up. They don't participate in the healing. They go to bed at night thinking that their parents are fighting because of them.
Stop complaining and be specific.
You need to stop complaining and start asking for what you specifically need from your partner. Tell him or her exactly what he/she needs to do in order to make you and your kids feel accepted and special. In turn, you need to ask your partner what is needed from you.
Mutually agree on punishment.
Don't assume that your style of disciplining will be appropriate for your stepchildren. It's important that you talk to your spouse about the rules and punishment that existed before you joined the family. It's unfair to change the rules on a child overnight.
Create a personal relationship.
Make a commitment to developing a relationship with your stepchild that has nothing to do with your spouse. Set aside some special time in which you and the child can interact alone. You also need to stop thinking of your stepchild as "his/her kid" and regard the child as an individual. Make no doubt about it, you are a pivotal person in that child's life.