Sorry, I meant to respond earlier, but got sidetracked here at home.
Okay. My DS2 & DS3 are almost exactly 3 yrs apart (5yo and 2yo). Our older 2 children (DS1 & DD) are adults and do not live at home. When DS3 was born, DS2 had just turned 3yo. He was already showing signs of difficulties, but we couldn't get any of the GPs at the practice to refer us anywhere. And it's not mild difficulties as when we finally did get to see the paed when he was 4yo, she said right off that he was a complicated little boy and he has since been dxd with ASD(HF), ADHD, DCD, hypermobility and sensory problems. So he can certainly keep us on our toes. (just to give you an idea of where we're at)
I had a horrible time with sleep as well, as DS2 was an incredibly poor sleeper who woke up by 5am every morning, and sometimes as early as 3 or 4am. DH worked nights, so not much help there. Take sleep whenever you can get it. Really. You didn't mention a partner, so wasn't sure, but if either your partner or mum or friend can watch the children even for a couple hours here and there, then take a nap. Everything is so much easier to cope with when you've had sleep. Sleep deprivation is the way to madness. There's a reason it's used for torture!!
DS2 doesn't follow instructions well either. We are slowly getting him into a routine with certain instructions, but it has to be the exact same phrase, with timed warnings, and ongoing encouragement, or it just doesn't work. Initially it may be a bit all over the place, but you'll start getting more comfortable and get a routine going eventually.
The big thing for me was to get over the "must jump when either of them fuss" thing. I know that sounds ridiculous, but sometimes DS3 would fuss while I was in the middle of doing something with DS2. As long as it wasn't going to be too long, and I knew that DS3 was okay (fed, safe, clean nappy, and such), then he can fuss for a few minutes and not come to any harm. If your DS2 is upset over the noise of the baby crying, perhaps you can get him some ear defenders so that it's not so loud to him. DS2 uses ear defenders a fair bit, although we didn't have them when DS3 was an infant (and they definitely would have come in handy).
As far as a walk is concerned, we have specific rules. It was a double pushchair initially, and while DS2 didn't like it, he got used to it. Initially he would kick off and I would just let him blow off steam while we were walking, and I would just keep chatting as we went along, as if he wasn't shouting. Eventually he just stopped kicking off over it. I cannot let DS2 run around a playground either, as he is impulsive and has no sense of danger/fear. He's 5yo now and I still can't do that. It does limit what we can do, I will admit. We try to keep the garden (fenced) fairly clear so he can run around there, but often it comes down to taking him to a local soft play to allow him somewhere to run a lot. (although he runs all over the playground at school as well now)
Going somewhere is arranged in military precision around here. 
School starts back up tomorrow, and I've already got everything ready to go for tomorrow. DH works early mornings now, so I do the school run by myself, with DS2 and DS3, which can be quite stressful if I don't plan ahead. Obviously at 5yo and 2yo, our situation is different, but just an example of how you just need to organise to suit what works for you. We have a Maclaren Major for DS2. He has hypermobility, but will either run or refuse to walk (yup, nothing like a complete about face, eh?).
So after discussing with the OT, we are making every effort to encourage him to walk safely. But because of his impulsivity, he must be held on to at all times outside. So he walks next to the pushchair, with a wriststrap on. If he tries to run off, he has to hold on to the straps of my handbag that's hanging from the pushchair handles as well. DS3 rides in the pushchair, but also has reins on. If DS2 kicks off, attempts to run off a second time, or refuses to walk, then DS3 comes out of the pushchair and walks (with me holding his reins) and DS2 rides in the pushchair. I've also got the pushchair loaded with school bag and cloth shopping bag with DS2's water bottle and lunchbox and nappy change materials for DS3. We leave early so we don't have to rush. And I spend almost the entire walk chatting with DS2, making up games with numbers and letters (which he is obsessed with) to keep him from obsessing over anything along the way that might cause him to run off or get upset (which could be anything, literally). Then I park the pushchair just outside his classroom, help him put away his coat, bookbag, lunchbox, and water bottle, and then wait just outside the classroom door (in case he tries to bolt from the classroom which he does fairly regularly) until his 1:1 gets there and takes over. Whew. That's it. Afternoon school run is everything in reverse.
It all goes relatively well now that he's used to it, but OMG the first day, I just about lost it, ended up at school 10 minutes late and looking like I'd been dragged through a bush backwards, hair all over, mussed up, stressed. 
At one point, I was screaming at DS2 to come back into the house (he was pulling his way through the door strapped to my wrist by the wrist strap), holding DS3 by one trouser leg (yes, I was sprawled on the floor), and dragging the dog back (who was intent on escaping through the open door) by the only leg I could reach. God only knows what the neighbours thought (they've thankfully never mentioned it, though I know at least 2 saw it 
). And I finally managed to get them all back inside, and regrouped. I learned from that - never ever attempt to load the pushchair OUTSIDE the door.. always inside the door with baby strapped in so you just have one child to control going out. I can laugh now, but I was definitely not laughing at the time.
Anyway, sorry so long, but don't worry. You'll carve out time for your DS1 as things iron out a bit. Just look for small bits of time (10 minutes here, 10 minutes there) to do something with him if you can. And I was always careful to take pains that the new baby didn't disrupt his schedule (as much as possible obviously), so he didn't feel pushed aside. DH still did his bedtime every night, so they had 1:1 time and I had time to feed the baby and such. You'll be fine, it's just a huge change, isn't it?