I don't get that so many of you are saying she probably spent the day trying to persuade her dd to allow mine to come, or it must have blown up massively or she must have been adamant my dd can't come.
I can see my dds not thinking to invite everyone, but they are not friends with anyone that they would be so distraught about them coming to a fairly large gathering.
You seem to see friends as interchangeable and amorphic, in a way that others don't.
If you've planned an activity to suit friends A-D, then having to shoehorn friend N into it doesn't work. Yet you might be very happy to spend time with friends L, M, N and O together, or A, C, G, I, J, N and O, or the whole alphabet.
What I'm hearing from you OP is that you don't understand people who do things differently from you, with your 'large family, more the merrier' dynamic. You don't recognise that that is one way of doing things, but one that many other people simply do not share; by habit, experience or inclination.
More than that, it's as if you're blind to those other ways of doing things. You don't see them going on around you, because you're so entrenched in your own way as 'the right way'.