Dr. Kim: Wow! That is such a great question and one that almost every blended family asks. The first really important thing you have to do is accept the reality of what you can do and what you cannot do. You cannot control anything done in the other home. You can control what happens in your home. Start there.
Prayerfully decide with your spouse what you want your home to look like and the values that are very important to you. You might even break these down into two groups. One would be the essential values that you will not compromise on. The second would be the values that are important to you but that you can have some flexibility with. Once you and your spouse are totally on the same page begin to implement these into your home.
Next, be consistent in your home and do not be negative about the other home. The second part of this is so important. My experience is that over time the children will see the difference in the homes and, more often than not, they will choose the values of the home that is fair and consistent and where they see that the values really make a difference in the lives of the family members.
Bottom line: Spend your time and energy on what God leads you to do and then lift the rest to Him in prayer.