Hi and congrats on your new one! You have a similar age gap to my two
(now quite a bit older!)
This age is exhausting, especially with a toddler too, and I think the best thing you can do for yourself is relax your expectations
. DS slept most of his first 10 weeks, and quite a bit beyond that in the sling, pram or car, and that honestly helped keep us all sane! We could get out to toddler groups, I didn't have to spend forever trying to settle, and it allowed us to concentrate on the emotional needs of DD which were arguably more important than the very physical needs of the baby. Obviously they need feeding, changing etc! But realising that independent sleep is the end goal, not the be all and end all from day one, is very liberating. Or at least I found it so!
We started trying for one nap a day in bed when possible, but I set a time limit on settling of 15 mins or so and if it wasn't happening, got DS up and stuck him in the sling. 15 mins for the toddler to watch a DVD was ok I figured, but probably not all day!! I also consciously decided to accept short naps and not bother trying a resettle unless it was clearly going to be quick and easy. Ironically DS is actually a far better napper than DD ever was! I didn't do shh pat in the textbook way either, as long as DS was happy in bed I left him to it and never tried to 'put' him to sleep unless he clearly needed help. Always the mindset of 'do the minimum'. I wanted and needed him to be an independent sleeper eventually but I figured putting the time in at 4/6/8 weeks was lots of time for little reward, by leaving it a bit later and out of the fourth trimester phase he got the hang of it pretty quickly.
I hope that's some use or encouragement!