M.F.
I can totally relate to your problem! My son had such temper tantrums he could scream for hours. Sometimes, he would end up falling asleep, and when he woke up, he would keep screaming about the same thing. In the supermarket, there was nothing I could do to shut him up, and I remember old ladies telling me "that child is out of control." Really? Well, why don't you try to shut him up then? Go ahead, I willing to learn how...
Anyway, he is basically Indigo through and through. He is here, not because he wants to be, but because he has some kind of work to do. He has most definitely ADD, even though he has never been diagnosed, he jumps like a kangaroo and gets incredibly distracted, so everything takes longer to accomplish. And, he is unbelievably psychic, both telepathic and able to see auras.
I had a whole shelf full of parenting books, and I also went to parenting classes, which by the way were nothing but a waste of time and money. None of those methods worked with him. Take away his priveleges - he doesn't care. Send him to his room in time out - he doesn't care. Don't give him any food until he finishes the food from his last meal - he doesn't care. How do you punish and mold someone who doesn't care? It doesn't work, it is as simple as that.
What did work, was to give him options, and full control. I made up a big container in the fridge with foods that he liked, and he just helped himself whenever he was hungry. When he got older, I also taught him how to make toast and omelet, which was very empowering. If he didn't want to go to bed, I told him that was ok, as long as I didn't have to see him or hear him, and he stayed in his room, and he was able to get up in the morning without my help. As I learned to work with him, instead of against him, his tantrums got much less. Punishment just don't work with these kids, so don't listen to anyone who haven't had one of these. They just don't know...
Now, he has become a teenager. He is very caring and likes to share, and he has become very independent and responsible. He is incredibly good with money and already has his own bank account, ebay account and paypal account, so he can buy whatever he wants on ebay if he has enough money in his bank account. And, he is also very good with computers.
All in all, he was unbelievably challenging for years and years. I felt like a total failure as a mom, and some days, I didn't even like him. But he has actually turned out greater than I ever imagined. So, just know, you have given birth to two strong little children who know what they want. These are good qualities to have in an ever changing world. They are probably here to bring in new times and change whatever doesn't work in the world, and their inner strength will help them do this. Just, don't compare them with anyone else, and whatever you do, don't dope them with medicines to make them fit in - that would destroy something that shouldn't be destroyed...