Hi OP, sorry you are having such a tough time, it will get better. I’ve only got 3 years between my boys, so the bigger one was slightly less aware of his life being torn apart, but completely relate to the issues you are having.
I’m sure you’ve got all this sussed already having had a reflux baby first time round too, but tilting the Moses basket/cot, and a stretchy sling helped me keep a grip on my sanity second time round, it scored me slightly more sleep, and it meant DS2 could be upright and snuggled during the day while I did things with DS1.
I also did baby massage with DS2 - I signed up to various classes as I hate the whole mums and tots dynamic and I do much better with an activity to focus on, and after my experiences with DS1 I knew it would help me to have things to go out and do. Baby massage is great for relaxing mum and baby and can help with building the bond between you.
Life will get easier when your DS1 is back at school, but until then, try and score the wins where you can, if baby wants to nurse all the time, then have a dvd session with DS1 while baby is nursing. I found that from a couple of months old DS2 would normally have a nap in his vibrating chair while listening to music after breakfast for about half an hour, and I’d make a point of telling sleeping DS2 that it was now DS1’s time to play with Mummy. I also spent a fair amount of time with a child either side of me sat on the floor, splitting my time between helping with duplo/lego creations and amusing the baby.
And recruit DS1 as your number 1 helper and praise him loads for every helpful thing he does with the baby, and sing his praises to the baby as well. It can seem like a strange thing to do, but it’s really paid off for us.
Hope you see the light at the end of the tunnel soon, and sorry for my long ramble!