M.R.
I've always felt that 3 is a lot harder than 2. My oldest is 4 now but one thing that helped him in the 3's was to have a chair that we sometimes called the "Crying Chair." If he was upset about something, whether it was a whiney or angry upset, I told him it was okay to cry and be upset, but he had to go sit in the crying chair until he calmed down or stopped. He sometimes played with it and would fake cry about nothing and insist on going to chair, but other times I think it helped him feel that it was okay to be upset and irrational (they are learning self-control at these ages and cannot be expected to just have it) but he knew he had to go "lose it" in that place. It also kept him out of trouble and helped him focus on calming down rather than other things. He still loses it sometimes (he has a little brother and they both lose it) and I haven't used the chair that way for a while, but it does take consistency, not being afraid to leave him alone (make sure his room is safe--my kids have managed to find everything we didn't think of to get into when left in their room), and try to keep calm yourself. I will sometimes just tell my oldest that I simply cannot talk to him right now until he calms down or it is going to make me upset, too, and then we can't talk. It does pass eventually, but I'm still in it sometimes.
Oh, my oldest also started doing better when I looked more closely at his sleeping patterns. He was not getting enough sleep between his very short naps (they were a major struggle) and I found he slept better and got all his needed hours at night when I stopped pushing the naps in the afternoons. His moods and emotions improved a LOT when he was definitely getting more sleep. When he hits a growth spurt he also has more "outbursts" and gets more tired and moody more easily.