R.M.
Hello Marshamona,
I specialize in behavioral issues in my coaching practice, and your problem is quite common. First a little education, children fight over everything often because they feel they need to battle for your attention. Whether it's "I want Mom to see my picture first" or "I want Dad to praise my report card first", kids have a hard time understanding the idea you are proud of each child for different reasons.
To ease some of the fighting, try the following:
1) Make sure everyone in the home is treating kids evenly without comparison. You may feel that you're doing this already, but sometimes little things get past you, like, "Bobby always gets the dishes done right after school, I wish you would get your chores done as quickly" or Sally has been really good lastly, so she's been getting just a little more attention.
2) Create household rules & consequences to the rules and allow the kids to add their rules too. This could be knocking before entering the room or leaving Bobby's Lego's alone, but this will help create consistancy.
3) Create a "no fighting" zone, and if fighting happens in the "zone" the fighters must leave the area until they can be nice. This goes back to the family rules. I explain that certain areas of the home are family areas which means all the family must be treated with respect. If a member cannot obey, they can go to their area, as in their room.
I hope this helps.
R. Magby