As others have said you are responding in a very (understandably) defensive manner. I feel as if you feel you have to defend yourself to everyone - headteacher, SS, mumsnet. Here's my tuppence worth (am student social worker in another country but no desire to work with children and families).
If the head brings things up which have been resolved, then just say that issue has been resolved. I would like to draw a line under it and move forward, as your mentioning it isn't helping the process.
For your own benefit I would write a list of everything you have done in order to put your children's needs first. No more relationships, given up job, cooperating with SS. These are all good things. Any time you put a new system in place (cleaning toilet when they are at school would be a good one) then write that down too. Take it to the next meeting. You can refer to it if need be, but knowing that you have it will help you feel more empowered.
Then write another list of what you feel you need help with. You say that you are exhausted from dealing with it all, and I dont think anyone would blame you for that. Can you get some relief fom SS? Ask them why it is taking so long? Can they follow it up? When are you likely to get it? Are there any alternative charities that could help? Asking questions shows you are taking an active part in the process and that you are willing to work with them for the benefit of your DCs.
I would also (if you've got the energy for it) try and find a support group for single parents, or parents of disabled children or whatever. Is there a sure start centre near you? Could you get some advice from them? Again, showing initiative shows that you want to do whats best for your DC. I would worry that you have no support network, what steps coould you take to get one? (MN local is not a bad place to start)
I hear what you say about hte goalposts being moved each time, but I think you could change the way you think about the whole process. Their goal isnt that you are unemployed and that your kids are surviving. Their goal is thriving kids in a functional one parent family. When they say do x, and then when you've done x do y, it's part of a process. They are giving you baby steps as part of a wider goal. Perhaps you could ask them what the overall goal is, and how they expect to get there, what your part in it will be and what they will do, and how they will measure that these goals have been met.
They need to document that these minigoals are being met. They cannot just take your word for it that you have no mental health problems. They need the word of a qualified professional. You are ill until discharged, not self discharged. Think of it from their POV what would happen if they closed a case on someone with MH problems because that person said they were fine, and they werent, and then they did something awful to their children. That is what they are avoiding.
I wonder if part of the problem is communication. Even on this thread you say one thing, and then when people respond, you say no I meant something else. I cant imagine how stressful it is to have SS involved, and I would probably get defensive too, but htey arent there to criticise, they are there to help. You dont always seem to understand how your behaviour can be interpreted by others. Do you get minutes of the meetings? If not I would request a copy of the file - although I dont know the UK law on how this would be done. You can take notes at meetings, and you can take another person with you too, which I think is a very good idea. If there is something in there that you dont understand then ask for clarification, adn write it down so that you can remember it later.