On point 1, for my 7yo party dm asked me to make a list of who I wanted to invite.
I didn't really have a close group of friends so I went through the different groups I was in at school, and invited the girls <boys yuck!> who were in those groups.
So that was the maths group, the reading group, the PE group, art group (we were grouped for everything).
I gave dm the list and she said it was quite a lot, and was I sure these were the people I wanted. Yes, they were.
She then asked if it was all the girls in the class, and I said confidently no it wasn't. She asked who wasn't on the list and I told her there were lots, but when it came to naming, we realised it was only Denise. Actually dm realised. I was adamant that there were several until I really looked hard at it. In my defence, we'd had a lot leave and join that year.
So Denise was invited too.
But if dm hadn't thought to ask, or had taken my initial response of lots weren't on the list, and she had no reason to disbelieve me, and as far as I was concerned I was telling the truth, then she would have been the only one missed out.
So it's certainly possible that both Mum and dd didn't realise that she was the only one.
But also if they are regularly having fallings out, and by the sound of it that's the case, actually as the Mum I wouldn't want to deal with it. It's really hard to deal with a situation when one is your child, and especially at their birthday. I think seeing as you are both aware of it, especially as you say your dd has a "strong personality" it was very sensible to not have her there.
I used to say to my dc divide invitations into three:
- Expect to be invite (best friend only, and maybe another)
- Hope to be invited
- Wouldn't expect to be invited
And if you get any invites after #1 that's a bonus. In your dc's case I'd have put this one as a #3.