Weddings are stressful regardless if the families have known each other for years or just a few months (I've even had some that haven't met until the day before!). Keeping those stress levels down to a minimum takes a little work, some pre-planning and worse case scenario an un-involved third party.
Couples can be pro active by introducing their families to each other, in person or even via Skype - have an engagement party, meet together for a holiday or a fun relaxed family picnic or BBQ.
Know your family - if one side of the couple knows that their family will be hurt or upset that they weren't the first told, the first asked about a detail, the first involved then give them those bragging rights. Ideally, each side of the family will be given information/asked questions at the same time (or as close as possible), but when that can't happen, take the high road and just reach out to the family most likely to be hurt first.
Finally, use that un-involved third party to help deflect the stress. If you have a planner or coordinator, let them know that there is the possibility of some stress and drama and tell them what the stressor is likely to be. We can't help if we don't know about the issue, but we are really good at taking care of it once we know about it.
Planning a wedding is stressful in itself, but then the thought of the blending of both families on a big day such as that compounds the worry. A couple things to stave off the potential stress is to promote the importance of everyone being their to celebrate YOU! “We are so blessed you could all make it to our wedding, this means a lot to us!” Also, be proactive. Plan your seating chart to keep certain members from others and open the line of communication a week before the wedding to air any concerns others may have. Respond before you end up having to react.