Firstly, if you work in education in any capacity, you really, really should be in a union. NEU and Unison both represent support staff. You need the protection in case a child makes an accusation of any kind against you OR a child has an accident whilst under your supervision. It's also useful to be in a union in case your role is made redundant etc.
Secondly, I agree with others it is reasonable to ask if you can bring your son in. However, you may be told no because a) the head has risk assessed for the exact number of children coming in and can't accommodate children of staff or b) because the head etc feels this might create bad feeling among parents, many of whom will be in the same position as you. Or for some other reason.
You are entitled to emergency leave to look after dependents, or unpaid parental leave. If you aren't comfortable leaving your son home alone I would look into this. Could any parts of your role be done from home on the day?
Final option is to try to arrange some child care for all or part of the day. Would any of your friends/parents of his friends/any of your relatives be able to have him for even part of the day?
In my opinion, it's fine to leave a sensible 11yo alone for the day BUT I don't think it's reasonable to go from leaving them alone for 30 minutes only, to leaving them alone for a whole day- presumably you won't be able to check your phone much at work or leave if there is an emergency.
BTW, you are very unlikely to be the only member of staff in this position so please don't worry about "looking bad" if you have to stay home on the day.