Dealing with stepchildren can be one of the most difficult things a stepparent will face. In fact, not knowing how to deal with stepchildren can be a major cause of stress and tension in the newly blended family, which eventually may lead to divorce. If you want to stand a fighting chance of making your second or third marriage work, then dealing with stepchildren properly will be something you will have to learn and face head on.
Being forced into a new family unit is not easy for most kids. They look at you as the evil stepfather or wicked stepmother trying to take away their natural parent. It will probably take a while, if at all for them to even like you at the very least. Don't take it personally. In fact, you should expect such behavior. Try to give your stepchildren the time and space to accept their new family situation.
Some kids find it so hard to accept and adjust to a blended family that they often rebel and test the limits of their stepparent. This is especially true when dealing with teenage stepchildren. Teenagers are at that point in their life where they are trying to establish their independence so they may find it hard to accept yet another authority figure.
In cases when stepchildren become disrespectful, it is important that you let them know that in your own home, you expect them to respect you. They don't have to love you. They don't even have to like you but they have to respect you and your rules otherwise there will be consequences. They can do whatever they want outside your home, but once inside, your rules are to be obeyed with no exceptions.
You and your spouse should lay out the rules early on and they should be enforced and applied to all the kids both natural ones and the stepchildren. While dealing with stepchildren is hard when blending families, you should not have to suffer in silence. There is no excuse for disrespect. Remember you are the adult and just as you expect respect from any visitor, your stepchildren should accord you the same respect. If despite all your best efforts nothing works, then maybe it's about time you sought family counseling.