A: Well, actually...not so simple! You sound very intuitive - and yes, he does sound frustrated and confused. It seems like you've hit right on the emotion.
Yes, this could be a normal two-year-old frustration topped with the delayed development...we see a lot of behavior issues in speech therapy. Speaking of, is he IN speech therapy? There may be something to the communication aspect that an SLP could address. At the very least, if you have him evaluated and they don't find anything, a good therapist should at least be able to give you some pointers on developing his communication at home. Also, if his hearing hasn't been checked, do that. If he can't hear, then he can't understand you, he will get confused, and he can't develop sounds and talk. Look into those two things first, and in the meantime, teach him sign language if you haven't already. He HAS to have some way to communicate with you or the poor little guy will continue to be extremely frustrated. He needs to know the basics: eat, more, help, milk, hurt, bath, etc. From there you can expand - and it's amazing what these little guys actually know but can't tell you for lack of communication.
Did you see the video on my website of the child using sign? She was about 18 months old at the time - and knew SO many signs. That was my daughter, and she was delayed in her language development (ended up in speech therapy!) but we cut out a ton of frustration by using signs. I remember her being in the car, trying to talk and I just couldn't understand her - and she'd get so upset and angry. As a speech therapist/mommy, that was heartbreaking. BUT, through the sign language, she was able to communicate so much with me, thus cutting down the frustration level. She was in speech therapy for a year when she was four, and now she's great...no problems whatsoever.
As far as your consequences, it sounds like you are doing the right thing, talking softly, but making him calm down, then apologize. But the root of it is the outbursts. It may seem like there is no trigger, but for outbursts like that, there has to be something. You are just going to have to try and step back and figure out what it is. Is it possible that he is in physical pain? Even something as simple as teeth? Could it be an allergic or negative reaction to any foods? When/if you rule that out, look at what he is trying to gain by the outbursts...and make sure he does not get it. THEN, and most importantly, you have to TELL and SHOW him how to act next time. Model the words and actions for him so he will know what he is supposed to do instead. And listen - he's young, so you will have to do this eight million times, but he will catch on. As long as he actually hears you (remember to check his hearing), this will help him tremendously. He is obviously very frustrated and doesn't know how to act or what to do.
Now, the waking up at night and thrashing/screaming...that's something you need to get to the bottom of quickly. I suppose it's possible that he's just overtired from the stimulus of the day. If so, the first thing you do is get him on a very regimented schedule. Same activities at the same time everyday. Make sure he is napping and getting enough sleep. Once you've got him on a strict schedule (toddlers love the security of knowing what comes next and what to expect) - and you are two weeks into it and he's still waking up screaming...then you need to dig deeper. Secure and happy toddlers are ones that get enough sleep at night, and if he's not, then you are spinning your wheels. Is he having night terrors? Is it phyiscal pain? Does he just want your attention, or is he truly asleep when he starts up?
So there are your starting points: check his hearing, look into speech therapy, teach him some signs, rule out physical pain, get him on a strict schedule, and figure out the triggers of the outbursts.
Good luck - you are an awesome Mommy, and I know you can do it!