Well it IS mad! Mine are 18 months apart and the youngest is now 6 months.
Somehow you all survive. But some days only just.
Tbh it is, at least for me, better than being pregnant and dealing with a toddler :)
Some days to be absolutely honest I really don't love it at all. And other days I think it's pretty awesome. And if you could see the two of them together now it would absolutely melt your heart. DD (the youngest) adores her big brother and grins and laughs at him. He took a while to adjust but is totally taken with her as well!
To begin with we had quite a biting and hitting phase. There wasn't really anything I could do that helped. It was just a phase. It passed.
I think key tips that worked for us that we got given are:
Be organised - do as much as you can the night before (to be fair we've struggled with this because DD has been colicky and then a nightmare cluster feeder)
Get out!!! Do stuff! It all goes a lot better the minute we get out of the door. And DS is far more manageable once he's been exercised as it were.
And everything is always better if you've had sleep. So rope in any help you can get to get any chance of more sleep! I guess if your eldest is 3 you will be getting the free nursery hours so at least you will have a break with only one to look after for at least 15 hours a week? It may seem remarkably easy at those times ;) and given my point above I would consider using that time to sleep. At least in the beginning.
It's hard but somehow you get through and you suddenly realise that you've had some fun too :) good luck!