The very first thing that you need to accept is that none of this is in any way your 'fault' and neither is it your son's fault. There also isn't any need at all for you to feel guilty for your feelings towards him - I'm sure you know that it's his conditions and needs that are causing such upset and frustration, not the boy himself.
Depending on circumstances (assuming he's still alive), I'd say there could well be plenty of fault lying with his other parent for not supporting you or his son, though....
He has the diagnoses, and they know full well what his needs are. Even if they DID for some outrageous reason think you an unfit mother, they are deliberately failing their responsibilities to help you cope with his needs, despite your persistence, so are in no position to judge you negatively - and if they don't want to help you, they're very unlikely to want to take him away so that he (his conditions and needs obviously) becomes entirely their 'problem'.
Not that it helps you at all, but your determination and managing to just about struggle through against all odds might actually be being used against you by them as an excuse to brush him under the carpet.
I know you probably won't want the attention, but you may have to start being less 'reasonable' about it. Get everything in writing wherever you can and put the ball into their court. If they say what he needs, ask them how they propose to arrange for this. If they say that it's another department/body's responsibility, ask them which specifically named person they're going to refer his case on to. If they say that it's not their responsibility, ask them exactly what/why it isn't and what kinds of scenarios WOULD be their responsibility. Go to the local press, contact your MP, Twitter-storm them if possible. Keep making it crystal-clear that you are a loving parent, but you are not a professional with the qualifications or indeed the responsibility to meet his educational needs. You will comply with their acceptable solutions all the way, of course, but you cannot and will not take the ultimate responsibility for doing their job.
Make it abundantly clear that your son has life-limiting disabilities and that, under the Equality Act 2010 and the United Nations (UN) Convention on disability rights, he has a clearly-defined legal right to be protected from discrimination in access to education, among other things. Every department that fobs you off without a 100% clear declaration in writing that none of the responsibility for action or referral relating to your son's specific needs legally lies with them (and why), ask them to whom you would need to complain for their apparent breach of this law designed to protect the rights of the most vulnerable people in society - and make it clear that you will report them and go public, even if they try and brush you off and make it difficult for you to do so.
You sound like an absolutely amazing and caring mum. Plenty of lone parents struggle a lot, even with perfectly healthy children without any complicating conditions or additional needs. You should not have to be fighting these battles on top of everything else you have to cope with in daily life. As far as you can, shame and expose these heartless, unfit authorities into actually doing their jobs and don't let them heap any blame or shame on to you. You're doing an outstanding job and your son is very lucky to have such a determined advocate for him and his needs.