My #1 was 3y 7m , and #2 was 1y 9m when #3 was born (now aged 5, 3 and 19m).
Personally I found going from 1 to 2 harder than going 2 to 3 as luckily #3 slotted in fairly well.
Double pram very useful (I have a city mini double and also a city select with two seats and buggy board, prefer the city mini though), as is a baby carrier (I like a sling for the newborn stage and now use a Connecta).
It's a challenge but especially when #3 is a newborn and you can put them in the pram or capsule and leave them a couple of minutes while getting the bigger two sorted it's not really any harder.
Having a routine for the week I.e. playgroup/ activities/ shopping centre with a play area etc is good as otherwise you'll feel like you never get out of the house, and having a fixed time to aim for helps (I always like to do a T- countdown so I know when I need to start getting ready, and then if we're ready early it's a bonus).
In saying that #3 still has their one day nap manipulated around school pick up time but I think as I was more confident as a mother I felt happier making little changes to routines to make my life easier I.e. all the children bathe together, then #3 goes to bed and the bigger too hang out in their pjs for a bit rather than running two bath times