I think you're both being unreasonable tbh. You knew 4 uninvited out of 14 would be an issue. I think you subconsciously wanted to exclude this child maybe, given your description of them (which honestly, I don't blame you in a way as it should be your DDs special day, not to be ruined by such behaviour). That being said, in a class of 14 I would have urged her to invite the whole class and make up the rest of the numbers from other clubs etc.
The other mum making a social media post is outright weird really. Despite what I said above, in situations where your child isn't invited to a party you just have to accept it.
Forcing friendships will lead nowhere and not everyone always gets invited all the time for many different reasons, it's just a part of life. Her taking to social media to essentially assassinate your character out of emotion is just purely childish and wrong. As a SEN parent in particular, I can see why she may be quite so upset but should have addressed it with you, like an adult, not make passive aggressive posts online like a teenager.
I think I ultimately would side with you on this one, I would be the adult and apologise to the mum who made the post and explain the situation, and that it wasn't done to exclude anybody, lesser yet her child specifically. If she apologises for the post then great, all water under the bridge. If not then you know where you stand with her. Just a completely avoidable situation though really, yet not the worst thing to happen in the world ay.
Hope your DD had a wonderful time