discrimination is in the unequal application of services / etc. due to inappropriate segmentation of the recipients...
discrimination is not when a service is not offered to anyone - just because someone is disabled doesn't mean they have a right to services not otherwise on offer.
I am not aware of any legislation that requires a school to provide parking of any sort - disabled or otherwise, I am sure that there will be schools in cities which have no parking at all. So no, YABU in querying whether they have a duty under the equality act - their obligations under that will probably extend no further than providing ramp access if needed should you turn up in a wheelchair - they shouldn't discriminate against you in the services they do provide (so access into the building for a parent), but parking is not a service they provide, so there can be no discrimination... in fact there is arguably discrimination in providing you with parking when no other parking is provided ;)
what you can do rather than reaching for the nearest lawyer to see if an act that doesn't apply can be enforced is speak nicely to the head as suggested above - and also talk to the council about whether there is scope for a disabled parking spot nearby... however as above, if there is no parking in the vicinity then there would be no discrimination in not providing a disabled spot and you would need to park where everyone else parks and if you are not able to walk, then a wheelchair is the correct answer...
the school have also been good in trying to help, but are now finding that it is not working for them - just because it works for you, you do not have a right to enforce something that doesn't work for them...
I do appreciate that it is not easy, however it is not easy for the school either - your thoughts are rightly focused on you and your children - they have to consider hundreds of children and parents / their needs / their conflicting demands... and ultimately cars where they shouldn't be is a huge health and safety issue for schools...