I'm so sorry you are feeling terrible.
I have 2 DC , one is 7 and one is 3 and I just could not imagine having another. Another and I would have completely NO time to myself, not even the tiny amount of time and space I get now.
Definitely get some help from your GP and whomever else you can think of. You are a good mum for sure you can tell from your posts, but we all have our breaking points and it seems as if you are surviving on very little sleep.
If you feel yourself getting very stressed with the children, put them in a safe place, put on some music, put earplugs in and go into another room with a lock (like the bathroom or something) and just sit quietly and focus on calming down for a few mins, even do it once an hour or so if you feel you have to. I've had to do this before, it's not ideal but better than completely blowing your top whilst you work on some strategies and getting some help.
I'd start by trying to get the baby's sleep under control, then sort out the finances and find out exactly what you would be entitled to in a split (because you say things are going this way) through CAB or similar. Then deal with everything else from there. Steps.
Using microwave meals (you do get relatively healthy balanced-diet ones these days), fruit the kids will eat, easy and quick meals and those cleaning wipes for a while should hopefully give you a little bit of extra time.