However, will it make the case worse given the fact that I was parked around a bend?
To a police constable enforcing criminal law maybe, but this is a civil law offence and the council cannot consider anything other than the legislation supporting double-yellow lines. This provides for two exemptions, (1) loading/unloading, and (2) boarding/alighting passengers. As I said previously, adjudications over the years since 1991 when the decriminalised laws on parking came into use, developed the "assisted boarding" concept as part of the exemption. So this is a well-established exemption that the council should accept. Clearly the CEO was not in error because there was nobody in the car at the time the PCN was served to the car, so the PCN was correctly served at the time.
The biggest problem nowadays is the wanton greed of councils for getting the PCN penalty money at all costs. So they game the system ruthlessly and invariably refuse informal representations. However, bearing that in mind, you should submit informal representations on the basis of taking your children to the school and the nursery, pointing out that you were unable to find a parking bay free. However, don't expect them to accept this. Only when you wait for the Notice to Owner, (sent to the registered keeper on the V5 Registration Certificate for the car), are reps considered with any degree of knowledge of the yellow line exemption. Yes, it is disgraceful, but for the time being we are stuck with this flawed law. I can only suggest you persist, and in the end you should win, but you have to risk the full PCN penalty to do so. That's how they make so much money, because few people like to risk the penalty doubling.