If she has any concerns, your friend should speak to the manager. If she wishes to raise a complaint it’s a simple matter of obtaining a copy of their complaints policy and following it. The policy should explain how to escalate the complaint if she is unhappy with their response.
The nursery may wish to review the relevant risk assessment with particular reference to supervision and consider whether door guards might be needed.
I wouldn’t like to second guess anything. Just because the key worker wasn’t present does not necessarily imply poor supervision. Neither does the fact that an accident happened. But they should consider the full circumstances. Trapped fingers can be very nasty or even result in fractures/crushing injuries. It depends on the type of door, but they must factor in the possibility that a similar incident in future could result i not a more serious outcome.
It has become quite common to make a big thing of anything that happens at nursery, but if the same thing happened at home people are much less harsh. Would your friend be considering taking action if this had happened on a play date/sleepover? If it happened at her home, would she think it reasonable for someone to tell social services?
As bad as it looks, this is a very minor injury from a medical point of view. Nurseries wouldn’t necessarily inform a parent before pick up time unless the child needed collecting early. In all honesty, parents will kick off if their childcare provider disturbs them at work.
I don’t quite understand the point about mum not being informed. She got the accident form and signed it. How is that not informing her? Have I missed something?