I'm so sorry. I believe I understand how you feel, yet I don't think you want adoption.
What you need is enough support to allow your DC to stay with you, and you still be able to feel like you.
Your ex is a useless arse. Does he know how you feel? Have you tried dropping the children at his and then turning off your phone?
I can't work out how you can highlight your desperation and need, without putting your eldest under pressure too. Has she told people at school that you are both struggling and she is worried? That may get some response.
Is your youngest at school or nursery? They also have an obligation to report safeguarding concerns.
I think this week you go to your GP saying you are suicidal and can't cope, and 'what will happen to my kids, how can I make sure my kids aren't the ones who find me' etc.
The problem is that you are presenting rational suggestions, like adoption, which detracts from the intensity and depth of your desperation.
I have been in meetings with SS where I have said I'm desperate, I need help etc. In my annual review it was written that I 'need to remember to ask for help'. Honestly! 
Is there anything else in this scenario that could change? Could you give up work? Could anyone else be involved in helping? Have you snatched every ounce of relief, without regard to how it looks?