Looks to me as though some of the information should not have been provided, but for a CV to be of use, the more information it contains the better.
On my CV, I do include the surname of the family, along with ages of the children.
Here is a typical example:
[From Date] ? [To Date] Nanny for three children aged 3, 4 and 5 at start
[Surname] Family
I was responsible for taking and collecting the older two children from school and the younger child to/from morning pre-school. During school holidays I would have all three children all day and we would enjoy outings such as walks in the countryside, visits to museums, steam trains, parks, National Trust properties and science centres (Intech & Lookout Discovery). The children especially enjoyed computing activities and we made an audiovisual presentation of a poem they liked. I spent 1:1 time with the youngest child in the afternoons, encouraging creative play and physical activity, which included a local playgym, Swimming and Ice Skating.
It does not contain the children's names. Where the children had specific medical conditions, then those may be mentioned - IF it was relevant to the job for which I was applying. A CV should be customised to fit the specific job for which the applicant is applying, thus if applying for a job working with children who have SEN, then providing details of previous experience of caring for such children, is relevant.
"judgement that a child developed more slowly because of a medical condition"
I feel that one is going a bit too far. Stating the medical condition would I feel have been sufficient - IF it was relevant to the job for which they were applying.