Sounds to me like you have your hands full--and they know it!
I agree with the PP that you need to very very consistent in discipline. (I don't however condone spanking, but that is a personal decision for all) No matter how big of a fit she throws you can NOT give in--EVER. All it takes is one time of giving in and they know that they just need to throw a fit for long enough and you will cave. Also, try to remain calm and firm if they are pitching a fit over you disciplining them. If they see you getting worked up, emotional, frustrated then they've found a chink in your armor and will work it as much as possible.
Each child will probably be different in what discipline works. Some kids respond to taking something they love away. My children (8,5, dd2)have to stand with their hands on the wall. (Our form of a time out chair). Yes, sometimes I have to stand right over them to make them comply. It's not for a set time either--it's until they can behave in the proper manner with the proper attitude.
Another thing that works is natural consequences. If one wants to pitch a fit over wearing a coat, fine. Let her go without. Soon enough she will be cold, and will know.
It's much harder to do with more then one, but misbehavior can have drastic consequences. Example: my son would pitch a royal fit in the grocery. One time, he wouldn't calm down, and I left the groceries at the front, took him back to the car and drove him home and put him in his room. He was so shocked that I would do that he never acted up again. It was harder for me, because I had to go back later and re-shop, but in the long run, it was worth it. Going out to the grocery is the priviledge, not getting a toy at the store. Not only did he not get the toy, he also didn't get to be "out".
I actually do that alot--the bigger the tantrum, the further away from your goal you are going to get. Kids going to fight over TV? Then no tv for anyone. ("Whoops, that didn't work") I do use peer pressure too-I don't care who started the fight and I don't want to hear the details--everyone gets the same punishment. That instills in them that they better work it out themselves and not come running to me to be the referee.
Sorry so long. To sum up: Be very consistent. Be calm and firm, not emotional. Natural consequences.