As @SMaCM says, children can get hyper after childcare, particularly when settling in. Usually it’s a short-term thing as they adjust to a new level of stimulation. Where it becomes a problem, parents should seek a solution in partnership with the childcare provider.
I don’t personally like carers being shut out of a nursery as an inflexible rule. Sadly, it is becoming more common: another ill-considered practice masquerading as 'safeguarding'. This policy is slowly creeping into more settings, frequently driven by the demands of parents.
However, I can see how a demand to inspect the premises for safety and cleanliness could go down badly: they are already inspected officially by Ofsted and EHO for that very reason. And, as @SMaCM points out, the child’s father had the opportunity to look round previously. By way of comparison, any grandparents asking to inspect a school would get similar short shrift.
In any case, I don’t see what purpose it would serve. You’re not going to find visible evidence of norovirus. There won’t be pools of poo and vomit. You won’t be allowed to check while they change a nappy.
Norovirus is extremely contagious and can be caught anywhere there are people. Places where people are confined together are particularly susceptible to outbreaks: Schools, hospitals, nurseries, playgroups, cruise liners, etc. An outbreak, never mind a single case, does not indicate lack of hygiene: norovirus is so easily caught, it doesn’t need dirty conditions. The fact that the nursery is in hospital grounds may well be highly significant, as you yourself suggested.
As your wife is a nurse, I’m very surprised you didn’t know this. Moreover, I am shocked that you didn’t report the diagnosis to the nursery at the earliest opportunity. Childcare and education settings have enhanced protocols which are put into place to counter these illnesses. Your failure to report may have delayed this and possibly lead to other people becoming ill. Again, something a nurse would surely be conscious of.
Cleanliness concerns should be reported to your EHO; concerns about care and welfare to Ofsted. I don’t see anything here that would get them out to inspect. Nurseries do have a regulatory obligation to inform parents about food and drink provided, but the regulations are vague about the exact details: it’s unclear whether that means a daily run down is necessary. They started telling you in detail on day three so, even if Ofsted felt there was a problem initially, they would regard it as fixed.