Oh dear honey, don't be down on yourself, you are not a failure at all. I'm sure you would hear from most of s that our little new borns needed to be on mummy or daddy, it is a very natural desire and reaction from such a young baby to want to be held, to feel the warmth, breathing and heart beat of his parents. Sure it's totally exhausting for you though!!!!!
I remember my NB being the same, we gradually got him used to the idea (really gently) of not being quite so close, so he'd fall to sleep on us on the sofa but we were a bit more 'hands off' by for example letting him get drowsy then positioning him by me so he could feel my leg rather than being constantly held. DP used to sooth him to drowsy then lay DS on his DP's lap so again he was on someone but not being 'held'. I also remember waiting until DS was in a deep sleep and laying him on a blanket on the floor, lowering my body down with him so we were still touching body to body, then slowly moving away. It didn't always work of course but over time it gradually got him a bit more used to sleeping without being held.
We also used the sling, which many mums here with 2 LOs seem to advise. Sling naps mean you are hands free to care for your older child and you can approach sleep training at a later date when your NB is a little older.
Whilst PUPD is not advised at this age you can begin shush/pat method which does involve picking up when baby is upset soothing until totally calm, drowsy or even asleep and then putting down and continuing to shush/pat in the cot. Initially you begin in arms with the shush/pat until full asleep before putting down and shush/patting to deep sleep. As LO becomes more accustomed to this you begin to put down a little earlier, so shush/pat to drowsy and nodding in arms then down into cot and continue to shsh/pat. Later you shush/pat in arms for the WD and put LO down sleepy but awake and continue. It's a process which takes time and which you keep moving forwards step by step.
Tracy said it took babies 20 mins to fall asleep and I found this spot on with mine, could set the clock by it.
I discovered (once I began doing this process) that DS needed to do the "seven mile stare" in exactly the same place each sleep and it needed to be a view he could see (almost the same angle) from his cot. Mine was doing his seven mile stare over our shoulder at a sharply contrasting dark/light plant near a pale wall...and then if he woke somewhere else he was not happy. Once I got him used to the seven mile stare from right by the cot (and even in the cot) he was happier when he opened his eyes, saw the same things, felt confident to close his eyes and go back off to sleep. I even hung black and white geometric shapes (stripes) from his cot side to give him something contrasting to stare at. It did help.
You might also want to have a look at DR Harvey Karps five s routine. It is very similar to Tracy's 4s and fits well with the BW ethos. I found it to work almost like magic and especially helpful in those early days or during 'the witching hour'.
If you decide to begin gentle sleep training I would suggest choosing one nap a day, try do the same nap each day because babies build habits, set aside some time to help her for that one nap, then perhaps sling nap the rest so you can do things with your toddler.
I know you are tired, but you are not a failure, you have a very new baby and a toddler to care for, it is hard work. Keep going, you will get through this. x
