Hugs! Yeah, I don't know why so many people were saying you shouldn't leave them alone together, because you obviously did not state that was the case. I would not have assumed that based on your post.
My DS1 was 33 months when DS2 was born and it was very, very, very hard!! Did I mention it was hard? We did AP and I felt like it had completely failed us. We coslept, but it became impossible to do so all in one bed. Anyway, I feel for you!
First, I was also going to suggest nursing in the carrier -- there is a wrap with the moby that allows you to be walking around while baby is nursing. My DS1 would sometimes forget that the baby was around when he was wrapped up in that thing on me and we were doing things together. It was almost like I was pregnant again.
I also did tandem nursing. I don't know how that is going for you but I was at my wits end. I gave DS1 2 months notice, and started to talk every day about how when he turned three he was not going to nurse anymore because 3 year olds don't nurse (obviously not necessarily true but something he could understand). We could not simply decrease sessions because he would not go for that, but we did limit it substantially. After a few horrible mornings with him screaming at 5 am that he wanted to nurse, with baby waking to nurse at the same time, I decided no more nursing until 7 am. So, he had to wait for it, as unhappy as he was about that (and he did eventually accept it). I also typically limited it to 2 minutes (with me counting so probably more like 40 secs sometimes, LOL!). Then, the night before he turned 3, he had his last session. It was very sweet. The next night, he asked, and I responded with empathy, talked about how much he liked it, how wonderful it was, etc. He cried of course but felt cared for. He asked again for several weeks, but the asking was less frequent. Anyway, every mom does what they feel is best but I think it is common to feel fed up and resentful with nursing the older one who gets so demanding for it, so something to think about.
Another strategy that I think can be very helpful is to try as much as you can to get in a positive cycle. What I mean by that is to try to avoid as much as you can the angry reaction to the hitting. If possible, try to respond very calmly that it is not okay to hit. No consequences right now, they are just fueling the fire. DD1 feels crappy about DD2 and it is just confirmed when she gets all the punishment. There will be time for that later. Instead, distract, distract, distract. Get involved in something else. Try to remain as cheerful as possible. Paint a smile on your face even if you don't feel like smiling. Catch DD1 doing something cool/funny/interesting and comment on it. Go even further -- narrate exactly what she is doing when she is doing anything that is not negative -- "Oh, look, Cherub is matching all the colors! Oh, look at the way you put that car in there! I see you have added some green marker to that picture, and that line goes all the way around," etc., etc., etc. Try as much as you can to get DD1 involved in things that you need "help" with. We didn't have success getting DS1 involved with baby stuff (doll, diapers, etc.), but he was always willing to press a button for us, or pull open a drawer because our hands were full, etc. It seems silly, but we do kindof ignore them when they are doing the good stuff, and give negative attention when they do the bad. So, if we can turn that around, they might do less of the bad for the negative attention.
Also, when you need cooperation and you get obstinance, one thing that worked a lot for us was racing. "okay, who is going to get their buckle on first! On your mark, get set, go!" Somehow that was much more the motivator than, "Put your buckle on." Make things into games/jokes whenever you can. I'm not a very jokey person, and not everyone is, but anything you can do to lighten the mood is helpful.
Also, this may not be popular, but you are in survival mode. There is nothing wrong with offering some chocolate to distract, or a tv show from time to time. It is only a short period that it will be like this, and you can phase any excesses out once things are more under control.
Hang in there. We had about 3 months of h*ll. At that age, they are naturally at a time of developmental change when they are learning to be defiant, that they have their own ego, and that you can't make them do anything. It is just compounded with the arrival of a younger sibling. You will get through it. Go easy on yourself, and try to go easy on DD1. After about 6 months, things settled down for us, then they got hard again around 12 months for a couple more months (as younger sib does more, infringes upon older sib once again), but then at 18 months things were pretty great. We still have our moments, but I find that the more I can foster joint fun activities, the more they bond and care for each other, and the less attacks we get.