I also don't understand why you're pursuing this.
The person organising the event is in charge. You've responded once, and been given a face-saving answer, which has left the door open for renewed contact at a later date.
All you've done by pursuing this is asked for a more blunt response, which closes the door.
You say you've had issues with this mother. Have you considered she may have issues with you?
You describe yourself as 'direct' and the other mother as 'passive aggressive'. Well, you know, people come in all shapes and sizes. The other mother may find your 'direct' to be over-controlling and bossy. Her 'passive aggressive' may be her attempting to evade being controlled, without rocking the boat for the relationship between your daughters.
What's more, you say that you are all, as a group, committed to sustaining the relationship between your children.
But is that true? For all of you? If you are committed to this, then it's your job to put the effort in to organise meeting, rather than trying to manage others to do that for you.
People resent and resist being reduced to instrumental extensions line that.
And by 13, the children will have a say. If there was only room for 4, and your daughter dropped off the list, well, that's what happens. Sometimes, you have to bite your tongue, accept the 'polite' excuse (which keeps the door open) and wait. Over time, things work out.
People don't neatly divide into 'mean girl, mean mum' versus 'innocent victim'. There are shades. Yes, this was handled badly - and it might well be that your daughter has slipped down the list - but the fact the mother offered the face-saving solution of another meet-up suggests it's not a zero-sum situation. Turning it into something big probably doesn't help.
And, again, if it's important to you that this group stays in touch, then the easiest way to make that happen is for you to organise them staying in touch.
For the others, it may no longer be such a high priority. Especially as the children hit their teenage years and begin to get a say in things.
It's not necessarily the case that no longer being interested in keeping company with a group of other children your parents have chosen is the hallmark of a 'mean girl'. We all have different tastes in people and those interests change over time.
If you want this relationship to last the distance of years, I would suggest you give it a bit of flexibility and allow for occasional incidents such as this. Including polite, face-saving white lies.