Looking back at some of your earlier posts, before you had your daughter, and comparing to what you say now, you seem a lot more emotional and are crying a lot now. The first thing I would suggest is that you consider whether you might have a degree of post-natal depression. Might be worth having a chat with your doctor just to see what his/her opinion is.
Next, reading this post, and the similar one about your son, it sounds as though you have a very angry little boy who is using bad behaviour to try and get what he wants. Now, you have to figure out what it is he really does want. My first guess is that he wants more positive attention. Yes, I know he's not going about the right way of getting it, but at only 4 he's doing the best he can. Has his behaviour been worse since your daughter arrived? Sibling jealousy? When I had my daughter my 2 year old son rejected me a little at first and demanded daddy. Kids often do this when mum has a new baby. Because I understood this I was able to change it within a few days, by accepting he had the right to feel that way, and working out what he needed to feel happy again around both of us. What is necessary is to make sure you reinforce how loved and special each child is. Try and make time to spend some individual time with each one. Also, let each of them spend some time with dad too. They need both of you; it's not a competition about who is the most popular parent.
When it comes to discipline make sure that you and your husband are always on the same page. Give the kids the chance to divide and conquer and they will take it. Make sure that you don't go over board by jumping too hard on every little thing. Sit back a little and work out what is really important. If the kids know who is in charge and what is expected from them I find punishments are rarely needed. Make sure that punishments are balanced out with praise for when he does things right. Sometimes we have to work hard to find the things kids do well when their behaviour is out of hand; but if you watch carefully there are always some positives. Even if it is just the fact they sit still and eat, notice this and comment on it. Don't look out for every harsh word he has for his twin - look for the rare moments of kindness and co-operation and tell him how well he is doing for playing nicely. Positive re-inforcement works wonders. Once behaviour improves you can make kids work a little harder to earn that praise but they have to get some to start with to want to earn more. I get the impression that you don't like this child very much right now. If he feels that he will definately play up. We have to remember that it is their behaviour at a given time we dislike, not the actual child. The behaviour we can change.
Don't try and get him to explain his behaviour, he is too young for that. What you need to do is be the one to explain how he should be behaving and why. E.g 'Don't do that to your brother it makes him sad.' No need to make it complicated. Give him instructions what to do instead. Yes, kids do need to be taught how to play nicely sometimes. Show him how to play co-operatively. Get down with the boys and join in and let them learn by example.
Finally, bored kids are often difficult kids. Be pre-emptive and keep an eye out before trouble starts. Get them started on doing fun things and keep a little encouragement going regularly so things stay on track. A good runaround in the park will also get rid of a lot of that negative energy.
Hang in there, you can turn this around.