Different parenting styles across two households can make discipline a difficult issue between parents and children. However, lax versus strict styles do not mean that one parent is doing things wrong or the other right, or even that your children cannot handle the differences. In fact, children can learn excellent skills in responding to different personality types.
The most important rules may not share the same details, but they should follow along the same general lines: stay safe (avoiding physical harm, such as no hitting, wearing a seatbelt, etc.), show respect (how to speak to one another, expectations for personal space, and so on), and keeping in touch so that all parties know of any changes in schedule and activities.
Since your children will have different expectations per household, keep both rules and consequences consistent and clear. Your children will be both safer and happier for it.
(Information gathered from “Blended Families: What About Discipline?” published in Your Blended Family: A Guide for Parents & Stepparents from Family Advocate.)