Olive - I have been there with DD1 and it is awful.

You are doing an amazing job!! I found using rescue remedy helped my anxiety somewhat. I also gave up on 'making' her sleep (ha as if I have/had any control) so if she didn't go to sleep after x amount of time then I bundled her into the pram and went for a walk. This may be harder with 2 kids tho. I also made myself go for a walk every day without fail to keep me mentally a bit brighter.
I wish I had not blamed myself for her sleep 'allergy' as it was seriously a waste of time and energy when I had very little to spare anyway. Do whatever you need to get through but be gentle with yourself too. Also do not listen to people who tell you to do things that you are not comfortable with - I went down a few paths I am not proud of and really regret it. Some babies are just not great sleepers unfortunately. DD1 here had ear infection issues and feeding/weight trouble early on and I think that this did not help.
Take care xxx