Hi OP, my situation is pretty similar to yours.
I have 3 4.5years apart each, and my eldest aged 9 has an ASD diagnosis and awaiting ADHD assessment.My second is 4 nearly 5 and I also have a 4mo.
My two older girls are pretty hard work! Love them to bits but they are strong willed, boisterous sort of characters and quite demanding.Eldest can be mature and independent but also due to her difficulties sometimes can seem much younger than her age- needs alot of help to follow basic instructions with routines etc and struggles alot with emotional regulation.Her and sister fight alot.
In general, 3 can be an absolute juggling act as sometimes everyone needs something at once, the life admin, mess tidying and washing are crazy and I constantly feel guilty that someone isn't getting enough of my time.Most of the time life feels non- stop.
The newborn stage was particularly intense and for those first few weeks i had to accept that the house would be untidy, things would have to wait awhile to get done etc, as baby needed constant attention....do you have a supportive partner and/or network? My partner is a great hands on dad and has a weekday only 8-4 job which helps.
However I would never change it.....We were on the fence for a couple of years deliberating whether to have one more (think i read every post possible on here about the 3rd child) and finally went for it, and now so glad we did and both wonder why we didn't sooner.I don't think i could ever have got over the feeling of wanting another....I thought about it every day.The girls can find it abit hard sometimes having to wait to have their needs met, but absolutely dote on their little brother.I shared a book with my youngest daughter called 'Sophie and the new baby' which was lovely.I think involving your youngest and preparing them is key especially if they are ND.
As PP said, in some ways I have found going from 2 to 3 easier than 1 to 2 aswell- already used to juggling multiple children's needs/supervising them and also my eldest is at an age where she can help more than when I had just two little ones with her and her sister.
We don't have alot of money or a very big house but we make it work.
I am abit concerned how I will manage things when my Mat leave ends but will cross that bridge when we come to it.
I think trying to wait until your eldest is in school, and has been for awhile (at least maybe halfway through reception year) might be a good idea.I found it harder having a newborn and my 2nd still at home for afew months wheras when 2nd was born eldest had just started school, but they are two huge life events for a child so if they can be spaced abit apart it would be less for your 4yo to cope with as school might be alot for him.