Ok, so first of all, you need a HUGE hug.
You are doing so well to be getting through each day without collapsing. From my perspective, of not having to be kind to your missing partner... he's abandoned his partner, 3 children and unborn child (now born). He just walked away and the only reason he could collapse and behave like this is that he knew you'd take over. I have a lot of sympathy for mental health illnesses, but not when they are combined with selfishness and nastiness (as one does not excuse or create the other).
He has dumped all his responsibilities and shown he doesn't care at all for his family, the people who he should love and the children especially, who deserve unconditional love and the absolute best parenting each parent can offer.
So he gets to drop it all on you.
And you get to deal with your own grief and heartache, and your children's hurt and confusion, and your pregnancy, and all the practical nightmare of suddenly becoming a single family of four.
You are hurting. Your children are hurting. Add in a child with sn and a new baby then honestly, it's an incredibly hard situation where you and the dc must be at breaking point 
So, first things first, you need help. Does Home start exist on your area? And what can your hv offer? And what about children's services for respite and parenting classes and anything else they can offer due to you having a child classed as disabled?
And, I kinda don't want to ask, as I get the feeling I know the answer, but is there anyone you can ask for help in rl? Family, friends?
I know it probably seems like loads of extra work and battling when you're at your lowest, but you need to start sounding that gong, before you collapse altogether...
And as for the rest, I think there's some great advice here but it needs to be altered to take account of you being tethered to a chair/ sofa/ newborn.
Also, I'd not go for a huge amount of high energy massive changes right now. I'd find a few small changes that make a bit of a difference and that you can really stick too - don't wear you out or set you up for failure or make life harder for yourself at the moment.
You can probably do a much better job of picking those few things but here would be my outside perspective... Id start with the nice stuff. Your family life needs to get rebalanced, and all the discipline and consequences stuff will be super important in that, but don't forget the other side of the see saw... increasing the good stuff.
I'd also start with the stuff that gives you back some immediate positivity as YOU need some gentleness and love just as much as anyone else in the family. If you go down, they all go down, so treat yourself very kindly and gently.
So here are my suggestions for the first little changes I'd make:
ONE. Find the good in everyday - even if you have to stretch the truth a bit to do so at the beginning!
They're getting so much of their attention fix through negative behaviours, and it will take time to change that, but one way is to start giving positive attention and hopefully some of the dc will like that better than the shouty stuff and you'll be laying the groundwork for tackling the tough behaviour later. So stuff like 'wow look at the way dc1 is walking so sensibly off the bus' or 'wow everyone, did you see the way dc2 put his food down so nicely' etc, tiny things, possibly grabbed and praised just before they go off and do something awful!
TWO. Help make snugly moments for each child and you. Put back the love!
Find tiny pockets of time to connect with each dc, especially the older ones. I know it can't be loads of time, or even completely by themselves. But you need, and they need, to start feeling love for each other again. It's so easy to forget the good stuff when everyday life is so bloody hard and the children are being so, bloody themselves!
So, a squishy snuggle moment every day, or a precious just for them mummy moment close to bedtime, or a super grown up mummy + me doing it together moment ... basically any ways that you can inject love and kindness and appreciation into each day. You need cuddles and love just as much as they do to be honest!
What about using the baby as a prop for bonding with the older ones, so turning the baby away from being a disruptive addition to something you and the other dc can bond over? Or even making things like counting out the peas into a saucepan ready for dinner into a super special grown up kid helping mummy in the way that the babies can't?
Thinking about all of you, is there anyway you can engineer loving kindness all together? Like, one big family squish at the same time each day, before bedtimes, even after lunch to end quiet time (if you can enforce a few mins of quiet time when you're at home), or whenever there's a lull or tempers are getting frayed (but haven't snapped yet).
Maybe a big family squish on the sofa where you all say what you're favourite bit of the day together was... or where everyone says one thing they like about another member of the family? I'm ripping off love bombing type stuff by the way if you look it up online you'll find lots of ideas :)
THREE ignore, breathe, distract.
So many great ways to address the negative behaviour that you can try over time. But short term, you could focus on yourself, and helping you control your feelings and reactions to the onslaught.
Angry shouting or upset doesn't work as an everyday deterrent.
Try to ignore what you can't deal with for the moment. And when you feel yourself losing control, breathe and focus in on yourself, don't focus on the behaviour, on your breathing and on calming yourself down. Reassure yourself: It's ok, it's not forever. You're a good mum. You're biding your time. They're good kids really. Etc etc
And then, just change the subject, distract them and start a game, or look at x, or, so who is hungry?! Races, songs, marching together... basically anything to break them out of the loop they've got themselves into.
Don't feel bad for not addressing the bad behaviour if you just can't cope with it. There's no rule that says we parents have to make a huge deal out of every bit of bad behaviour or naughtiness. Consistency is great, but not at the expense of your sanity and your relationship with your kids. It's ok to ignore, just don't react to it at all, ignore, breathe, distract... and move on.
Final note in this crazy long post! Personally, I don't think these nuclear war stand offs work either. Where the punishments go up and up until you're locked into worse and worse punishments and upset on both sides. And the confrontations where nobody can ever win and it becomes about who dominates who, and who is prepared to push it farthest. Not kind and not helpful.
I agree it's important to carry through your promises, but I think it's more important never to make promises, and punishments, that you can't keep. Don't say punishments when angry as you'll end up with these big punishments you feel you have to stick to. Punishments that end up punishing you too!
Good luck, I know it's so hard for you right now, and I know it's not fair, but you're so tough to even be surviving, let alone trying to find ways to make it better x