The question suggests that you do not get along with the family at other times during the year, so there is no magic bullet to make everyone behave. However, there are steps you can take to make your holidays more serene.
As an addictions counselor, I suggest you begin with noticing how much alcohol is being consumed by your family members. If this is a problem and Uncle Bert or Aunt Neddie usually gets angry, unkind, sloppy or critical when they drink, avoid them. Make sure you slip away. Doing the dishes is a great way to limit contact and also make points with the person who did the cooking. No one will pull you away from the kitchen sink.
Being overwhelmed with holiday preparations can make many people short-tempered. If you see mom or dad losing their sense of humor, be more helpful. Anticipate what you can do to take a few errands off their shoulders. Wrap some packages, peel the potatoes, get the tool box for dad so he can put the jungle gym together. Be supportive. Be helpful.
If the whole family being together is just a blending of many strong personalities, don't feel you need to challenge every remark that is made. If you don't agree politically, say to yourself, "how important is it." You won't change anyone's mind. If your older brother is a know-it-all, let him rave. In your head say, "I am going to let go and let God." He's not your problem unless you get suckered into the debate.
Gatherings can bring out the best in us or it can unlock a lifetime of irritations with people. Choose, yes choose, not to get involved in unpleasant conversations. Change the subject, walk out of the room, make a phone call....do something to keep away from toxic people and toxic topics.