i am hearing you - i have just had 2 days like that & i have the stroppy 2yr who decided on the weekend he wants to start TT - i wish i could split into 2 actually 3 so at least one of me is sleeping lol.
All i can suggest is whenever possible let bubs sleep on you 5-10 mins is better than nothing and you can still interact with DD reading stories or bouncing with them when u r trying to settle bubs. And if you have to put him down & let him cry go for it - like everyone says we need our rest as well.
Good luck i hope you have a better day tomorrow