It absolutely will get better, & your toddler will learn to sleep by herself. I had 15 months between DS1 & 2, literally nothing could have prepared us for how different they would be. DS1 was a champion sleeper, by comparison to DS2 very easy going, did what he 'was supposed to' by & large. DS2?! Hideous reflux, constant screaming, tongue tie, CMPA, constipation, cat napped, would only (& I do mean only) sleep if cuddled up next to me. I felt very much like you do now & had some really, really dark moments & remember feeling broken by it.
I didn't co sleep with DS1 & would always insist on him going back to bed / sleep in his own bed. Following the arrival of DS2, that went out the window & if needs be we all ended up in bed together (DH works nights). DS2 slept in our room until he was well passed 2 & more often than not ended up in bed with me. We moved him in with DS1 who thankfully can sleep through most things & he'd still wake up, sometimes he'd be happy with a cuddle in his bed & at others he'd end up back in with me. Eventually at 3.5 yrs he started to sleep through, no sleep training, just started to do it & gradually the nights he'd wake became less.
We still have nights even now at 4 when he wakes because of a bad dream, finger hurts, poorly etc. & sometimes it's both of them & they're happy to go back to sleep in their own beds, each other's or we all end up in mine. Whichever, it's fine.
You are not fucking this up, you are doing what you need to do to survive. It's hard, relentless & feels never ending now. You're still recovering physically & mentally from a difficult pregnancy never mind having given birth only 9 days ago. Be kind to yourself, whatever gets you all the most sleep with the least stress (& is safe) is completely fine & will not break your children or mean you have failed in any way. You need to look after you in order to be able to look after them.
Big hugs OP.