doggity Not misunderstanding the law, organisations have to make reasonable adjustments where they are needed to allow someone to use a service etc.
For a school, parking is not a requirement in offering education, it is a benefit or bonus, and there is theoretically the ability for the OP to park on yellow lines outside the school, equally the OP could gain access via wheelchair, it is not a requirement that the OP can drive there, simply that the OP is not blocked from getting there... so there is no legal requirement for the school to provide parking to assist as it can be seen that there are several options already available to the OP... if parking was a requirement then every high street shop would have to provide parking - but that is not the case... The OP has access without having to park in that specific spot... the fact that others might be parked illegally on the yellow lines preventing the OP from parking there doesn't create a need for the school to provide parking elsewhere
However, as you mention, many places do help, not because they legally have to, but because they want to help with good customer service. In fact one of the best outcomes from the equality act was to increase the awareness of needs resulting in decent organisations helping...
The reason for my initial post was because the OP referenced the equality act in her original post, however I think that seems to have been out of frustration, (understandable) and that is not the route she is taking, but in chatting with the head, the focus should be on ways the school can help as both want, without causing issues for the school as a result...
Trying to suggest that there is a legislative obligation for the school is only likely to cause issues, I think that any school receiving such an approach would simply tell the OP to park on the yellow lines, or bring a wheelchair, and if no space on the yellow lines, talk to the council... however a more gentle approach on how the school could help without creating other issues, should be far more constructive...