Thanks to Mike & Tracy Collins for answering this question. Here are their thoughts:
Our first thought is to check your boundaries to make sure they aren’t overly strict. Ask a trusted friend/mentor about specifics. Looking back, we were too strict on some issues.
If you feel you are balanced in your boundaries, then your main priority in any situation is representing Christ. We represent Christ in our marriages by how we treat one another, to our children by disciplining them with both love and firmness, and to our families by being humble & gentle (Ephesians 4:2).
Ask yourself, why is this an issue? Are their children making yours misbehave? If so, your responsibility is to parent your child through the situation with the boundaries you’ve established for your family, not worrying about what other family members think. However, if your issue is that your family members need to parent with better boundaries (which very well may be true), you need to check your motives because you could be perceived as being prideful. Remember that your goal is to represent Christ, and you do that by being a humble example as you lovingly parent your own children.
Several years ago we were perceived as being too permissive with our children by some close friends. Our two families were sharing a beach house for the week. By the time we left, the difference over parenting styles had caused tension and distance between us. The one thing we did not do was have an honest conversation, which would probably have kept us as close friends. Being open and up front can often avoid hurt feelings.
One of the main things to keep in mind is your goal in parenting – a changed heart. In many cases, God uses these opportunities to change our hearts as parents! This may be an area where God is giving you the opportunity to represent Him through loving your family members, being patient with them where they are, and allowing Him to change them.