Dragn,
I feel your pain, I really do. I am betting that your kiddos are not on the spectrum, and are in fact extremely bright.
I have a 16 yo who walks a very fine line with aspergers, also has ADHD. He is brillian beyond measure, and had significant speech delay. (This was caused by his brain going faster than his mouth could work). He was very much like what you are describing with both of the kids behaviors.
If he wanted something he was unrelenting, and he was smart enough to figure out how to get around things everytime. God forbid any boundary ever be broken, like with the milk fit for your? He would then elicit that same response for the next 5000 times he wanted milk. Seriously.
I think you have a combination of issues here, you are exhausted, and with them most of the time. YOU need a break. Hire a sitter for a few hours at least once a week. This gives you a chance to reset your engine. They have discovered that they are getting pretty much what they want by screaming, and fit throwing, the little guy saw it work for his sister, and thought cool, I can do that.
Raising kids, and training pets are very similar in many ways. The need hard boundaries, rules and limitations. They also thrive on a structured routine. Have you ever watched Cesar Milan the Dog Whisperer? He does and says a lot of things that make sense for kids as well.
I was militant about bedtime. I had a very strict routine that I did not vary, even on the weekends. After dinner they got to play, at 7 they got baths, and jammies, at 7:30 they got a bedtime snack, usually some cheese or yogurt, something low in sugar for sure. At 7: 45 up to their rooms, and in bed, a quick story, and at 8pm lights out for them. Quiet rooms, with white noise machines so our activity in the house didn't keep them awake. If they came out of their rooms for silly things, not real things, or came out multiple times there were punishments. They were fairly warned as well. If you come out again, then tomorrow you can't watch teletubbies. You have to provide a punishment that has impact on them, and for some kids timeout is useless.
The bad news is it will probably be even rougher for a few days as you start to implement being much stricter on whats going on, the good news is they will respond, and be happier, and easier to manage. The even better news is they will get older, and this will become less of an issue. Mine are 14&16, and they both know that 9pm is bedtime, no if's ands or buts, and it's never a fight or battle, even in the summer, now they may read half the night, but hey it's summer break. In fact about 50% of the time, I don't even have to say it's bedtime, they know, and they go.
I am in agreement about having them tested, but don't be surprised when they won't do much to help you deal with it. My son was clearly ADHD, and if he were a little guy now would have been pegged as Aspergers too, very tactile/upset in routine created horrible fits/stimulation of multiple things was too much for him.
They refused to give any meds for the ADHD until he had behavior issues at school which was the second week of KG.
((((and strength))))