I second the terrible twos actually taking place when the child is three...my niece did it and now my son does it...he turned three in June.
THE SAME THINGS ARE HAPPENING...one minute just sweet as can be then all of the sudden he throws something or hits someone or runs away screaming no, I don't want to, you stop that.... (SO FUN!!!)
I thought it was because daddy works more in the summer so he doesn't get enough daddy time...but it didn't matter either way. I think really it didn't have anything to do with daddy working more, just to do with me being with both kids by myself more putting more pressure on me, so I searched for a 'reason' for his phase....because well how could my sweet little boy just whap his baby brother in the head like that and run away....
When daddy is around...then things that usually go smooth as butter for me, are difficult to do, such as bed time. When his dad is home I have so much trouble even getting him to go into his bedroom...then he doesn't want to pray, then he needs something. Then the daddy will sugar coat the I NEEDS, and get them for him...
We do the one warning then he has to 'stand in the corner' (oh my does he not like to stand in the corner). With time outs he doesn't really mind, odd but he doesn't, then with last resort he has to go to his room WITH the door shut...that is if he just will not stop misbehaving at all. Usually the corner works, then again in about an hour he will get threatened with the corner again...but their thought process doesn't last forever and a lot of times we will have to repeat ourselves, but stay consistant (I have heard that is the KEY!!!)
I am pretty sure your experiencing a phase just like we are...don't worry they are only three for a year :)