Nobody enjoys living in an atmosphere of conflict and stress. Unfortunately, that's the norm in many families. While conflict is inevitable when people live together, it doesn't have to be the defining feature of your home.
The first step in establishing a peaceful home lies in recognizing that when we are in a family, we will constantly be bumping up against people who are different, often difficult, and who are not going away--we are stuck with each other. This goes for all the relationships--between husband and wife, between siblings, and between parents and children. We grate on each other, whether we intend to or not, simply because of our differences. In fact, conflict is too often our default setting.
When we acknowledge that this is true, we can begin to take the next step, which is to adjust our expectations. Ask yourself what your expectations really are. If you're surprised by interruptions from your toddler while you're trying to get work done, or are surprised by your children's terrible behavior when you go to a restaurant, or expect to relax on vacation just because there are things for your young children to do, your expectations need to be adjusted.
Just as you accepted the fact that conflict is natural and inevitable, you have to recognize and accept the limitations of your children. You can't expect the same behavior from a three-year-old that you can from a six-year-old, and your six-year-old is not capable of twelve-year-old behavior, and none of your children are capable adult thinking or behavior (and honestly, if you haven't taught them how to behave well, you really shouldn't expect them to!) Know your children--recognize their tendencies and anticipate their behavior. Recognize the limitations of their particular ages, and adjust your expectations.
When you've recognized and accepted human nature for what it is (selfish), and accounted for the individual personalities and capabilities of your particular children, set up your family currency--the means you use to make exchanges within your family. Do you hear angry exchanges much of the time, or whining and complaining, or taunting? You need to establish a different currency. Announce it to all members over dinner--"From now on, in our family, if you want to be heard and answered, you're going to have to use the language of respect. Here is what it will sound like . . ." Then demonstrate. You'll need to be very careful always to use it yourself from now on, and insist your children re-state angry, demanding, or whiny exchanges respectfully. Don't waste time on "who started it".
Will this eliminate all future conflict? Absolutely not. This is just the beginning, the foundation for building your family culture. But you have to start here--you have to remember the human tendency to feel distaste for the "other-ness" of anyone who is different, and be realistic about the tendencies and limitations of each family member. Use this understanding to demonstrate loving patience with your children as you do the daily hard work of gentle instruction and correction. And you really must be patient--this is a long process.