Next time you go to the school, take some pictures of the signage and show us.
The school telling you that they cannot do anything about it and that you should contact the parking company is a "shrug off", especially as it is likely that it is the school that have contracted them in the first place.
Contacting Parking Eye will be about as useful as a poke in the arm with a sharp stick. They are only interested in one thing... your money. It is the school you should be complaining to about being invoiced for £100 by a third party, especially as you are probably charged by them for extracurricular activities anyway.
As always, Plan A is the best and simplest option. Perhaps go higher up the management food chain with your complaint to get more than a shrug off. Plan B is appeal to PE and hope your "mitigation" pull at the heartstrings of a ruthless company that is only interested in how much they can squeeze out of you. Plan C will be an appeal to POPLA if/when Plan B is rejected.
Unless you can convince a POPLA assessor that their client, PE, have issued the PCN in breach of any law or BPA rule,, then that is doomed to failure too. But never mind. A POPLA loss means nothing in the scheme of things. You would then be in limbo until/when Plan C kicks in.
Plan C is a court claim. Recent history shows that for a single PCN PE will do on elf two things. They will either farm the claim out to external debt collectors, most likely DCBLimited. They will add £70 to the clam and send you a load of useless letters threatening all sorts of nasty things like a CCJ or bailiffs. It's just words and they are powerless to do anything in reality. Eventually they will bring in the other arm of their business, DCB Legal who will eventually send you a Letter of Claim (LoC) and then an actual claim. This is actually good because it is 99.99% guaranteed that f you defend the claim robustly using a template defence, they will, eventually, discontinue the claim and then it is over.
The other possibility is the PE will issue a claim themselves, without using a third party solicitor. This is also good because they have, in the last year, been adding £20 to the original £100 charge which is not allowed. They have been so successful adding the £20 charge because the majority of victims who have not discovered their website of the MSE parking forums end up paying out of ignorance and fear, that they have now increased the add on to £25.
Whatever you decide to do, if you are adamant that this is an unfair charge and ou are up for a fight that you have a good chance of winning, then follow the plans described above.