111

It is not getting easier is it? It seems like there is a good dose of buck passing here. I remain concerned that they are telling you effectively to lie to get something to which you should be entitled if the medical evidence is sound enough. I may be wrong but I get the impression that 111 are not fully understanding the situation.
You can fight this going back and forth between the two for some time, but you need good professional advice. Thus I would suggest that you talk to your union if you are in one , failing that talk to a solicitor. The cost of that may be covered through the likes of the AA, or household insurance, who often have legal schemes attached to their policies.You can try 111 for a third time, and see if you can get a confirmation of the recommended action , or indeed a third option.
The advice from Unison can be found here https://www.unison.org.uk/coronavirus-rights-work/, and of course the useful contacts above by my fellow moderator, are essential to use if you are going to make progress. I would also encourage you to talk to your employer who has a duty of care to you for both physical and mental health. It is clear that the situation will be extremely stressful for you and you may be surprised at what they can offer. I would also suggest trying to get some support from the Neuro unit that your son attends, or has attended. They may not be operating as a unit but the staff will be available to help with telephone calls or emails.
If none of those gives you an honest answer then do please come back to us. as you say you have a couple of weeks grace at the moment. I do understand how you feel about this to some extent. My wife works in A&E and comes across all sorts of folk including like those you have described. From my point of view I would not for one moment , suggest she gives it up but it is a worry for me if she were to bring it home.
AS to the other point. you mention about making sure your child gets the best possible care, I believe your last sentence says it all. Regardless of the difficulties that you will face it appears from that sentence that you will do all in your power to keep him safe and well. What more cold he want? My child was not diagnosed until he was around fourteen, so I cannot advise what it will be like for a three year old. Pretty much since that time both he and I have been left to our own devices, and to try and find help when it was needed. on the MDUK help lines, on this forum and even on Facebook, there are some tremendously helpful and knowledge people who can us ually guide you in the correct direction. You will learn much along the way, especially that you need tenacity and perseverance. You clearly have those traits in good measure. WE will be here for as long as you need us.

Mike