In due course I comment in more detail on your lengthy post as it contains numerous inaccuracies. But this one I can mail straight away.
A 4 year old child is most definitely NOT considered to be vulnerable in the context of child protection or COVID-19 simply because the are a 4 year old child. They would only be considered vulnerable were that child to have certain underlying health conditions or where there were specific safeguarding concerns - as far as I'm aware neither of those apply to Cummings son.
As you may or may not know I am the owner of a nursery - and when we were required to close we were allowed to remain open for the children of key workers unable to look after their children and children legally defined as vulnerable. We have about 30 4 year olds on our books - not a single one is classified as vulnerable in the legal context which is what would apply in terms of justification of breaking loach-down/self isolation.
The government has provided guidance on who is, and is not, considered vulnerable in cover-19 terms - it does not include 4 year old children.
I did not mean "vulnerable" in terms of more at risk of getting very ill from Covid-19. I meant vulnerable as in at risk of being physically harmed and needing looking after because their age meant they cannot look after themselves or protect themselves from harm. In this context, anyone with an ounce of common sense would consider a 4 year old child as being vulnerable if both parents were too ill to care for him - though they are not vulnerable in Covid-19 terms of "at higher risk of severe illness"
https://www.bbc.co.uk/news/health-52784152ETA: The day after lockdown began, 24 March, the deputy chief medical officer for England, Dr Jenny Harries, clarified who could look after a child if both parents or carers were incapacitated.
She said: "Clearly if you have adults who are unable to look after a small child, that is an exceptional circumstance.
"And if the individuals do not have access to care support - formal care support - or to family, they will be able to work through their local authority hubs."
Any of the government lockdown guidance can be overruled by safeguarding concerns, or prevention of harm, Dr Harries said at Saturday's briefing.
She used the examples of an elderly person with no supply of medication, or a child with both parents too unwell to provide medical care.
"Risk to life" would be a valid reason to break lockdown rules, Dr Harries said.
When Dominic Cummings decided to travel from London to Durham, to stay near his relatives for support, only his wife was displaying coronavirus symptoms. So, he could have cared for their child himself.
But Transport Secretary Grant Shapps said at Saturday's briefing that the welfare of a four-year-old child was the main thing. He said Mr Cummings' actions had prevented the child from being without any support, should things have become worse.