I have 3 gorgeous DCs.
DS2 is 10 weeks old, he is my "easy" child at the moment 
DS1 is 7 and is a lovely, thoughtful, kind boy (flip side of this being he is very emotionally aware and sensitive). His behaviour with anyone else or at school is fantastic. At home, he's pretty good and can be helpful but he is also quite rude at times, goes on the computer/phone/ipad without asking, teases his little sister. All of these things are little but when I tell him off he hates it so it then escalates into him getting really upset.
DD1 is 4 and a gorgeous, cheeky, funny little madam. Again, perfectly behaved outside the house. At home though she tantrums a lot, screams and hits her brother (although this is usually after he has teased her) and cannot be told anything!
With DS2 being so small he is demanding a lot of my attention but I am trying to make time for each of them, unfortunately it feels like when we finally get time together something happens that means it all ends in tears.
I want DS1 and DD to stop fighting so much, for them to be able to play together while I put DS2 to bed/feed him. I want to effectively instigate a reward/(punishment?) system that works. We have had reward charts before for specific things (staying in bed etc) but general "be nice" ones are difficult to maintain, how could I do it? What if I don't see the bad behaviour? What if they do one thing in a day.
I don't really know what else to say but hoping for some words of wisdom please! Thanks