D.B.
First of all, L., if you work full-time, then your life cannot be dedicated to your boys. YOU work! It sounds to me that your 3 yr old is experiencing some difficult times and expressing his emotions in ways you disapprove. The child is 3 yrs old, still a baby in many ways. He has separated parents, the main parent working full-time leaving little time for showing him affection, a new baby brother sucking up alot of mom's love and attention, and a myriad of other changes going on around him no doubt. He is behaving normally for a child his age. Although his behavior cannot be acceptable it is a 3 yr old way of expressing oneself.
He's saying, "HEY somebody notice me! My life is in a shambles! I don't understand it. HELP!
You must be consistent in whatever method of discipline you use. I know you arrive home tired from working all day. I know you are sometimes, maybe all the time, feeling overwhelmed with the responsibility facing you each night. I've been there and done that. The only difference in my situation was that I felt truly alone. I didn't have the connection with my ex-husband that would have been helpful to our children. Also, we lived in separate states 3 hours apart. Therefore, I was raising three (3) by myself with the oldest being 9 yrs old when we split! The youngest was 4 and the only girl. Talk about chaos, ill feelings, overwhelming sensation to yell out for a Calgon bath!
You must discipline all unacceptable behavior and be consistent as to what is unacceptable. I used a chair for all kids who stomped, kicked, yelled, screamed, hit, etc. You must remain in that chair for as long as the bad behavior persists. Even excessive crying for the sake of getting what you want, deserves the Chair! Sometimes it takes more than an hour of replacing the stubborn child in the chair. You can accomplish nothing else because you must be persistant. BUt you do whatever it takes to make your point clear.
The point is: There are better ways to handle ones angers without all the yelling, kicking, etc. Let him know you will gladly give him the attention he needs AFTER he stops the bad behavior. Then be sure to follow through and give your undivided attention to share in whatever he wants of you after the crying and tantrums stops.
I had only one who threw tantrums. Initially I walked away, out of the room and continued on with what I was doing. If the tantrum became abusing a sibling, then I felt other measures of discipline were required. I followed through on what I said I would do.
Never make threats knowing you will not follow through. Eventually those fall on deaf ears.
BE CONSISTENT! And consider this baby is going through alot and has no way of expressing his feelings other than to do what he's doing to get your attention. Take a step back, deep breath, and show some loving attention before resorting to more drastic measures. GOOD LUCK and GOD BLESS your little ones & you!