I imagine the child wasn't having an asthma attack though seeing as the mom then took her daughter home when the doctor wouldn't see her. I'm pretty sure the mother would have called an ambulance if her daughter was having an asthma attack in light of how seriously ill she'd been in the past. I'm assuming the child was in a relatively well condition seeing as the mother accepted the decision to take her home and bring her back the next morning, if the mom had serious concerns about her daughter then I imagine she would have gone to A&E.
The report says the child died five hours after being turned away from the GP surgery and she couldn't have been evidently getting worse in that time frame as otherwise surely the mother would have called an ambulance at some point before it reached the point of her having a seizure and stopping breathing?
It also says the school first phoned the mom in the morning yet if the mom was happy to wait until 5pm to see a doctor then the little girl couldn't have been acutely too unwell as again, I would assume the mother would have gone to A&E if she thought quicker medical attention was needed.
I think there are a lot of details we aren't being told, there's a lot of room for speculation and like most things this probably isn't as black and white as it appears.