Thank you everyone for your replies, lot to think about here. In answer to some of your questions;
The other girl is not a bully. She was showing off to her new friends and used my daughter as the punchline. Some off hand comments and belittling. Asking in front of a group my daughters scores as she knew hers were higher then laughing. Asking about holidays and family things she knew would appear below her own and laughing. My DDs name always being the punchline to things. DD asked me not to speak to the girls mother as they were such small things that it seemed petty and they could easily be denied. We discussed how she could deal with it herself and she did. I do not think it was bullying - I think it was a 12 year old girl turning a corner and trying to impress her new friends. It did not last long and DD did stand up for herself and spoke back to the girl. DD is very naive and did not help the situation. She spoke to friend about the behaviour directly and friend said it was not intentional and asked for some time apart. DD panicked and did not leave her alone. She did not contact her out of school but would essentially follow her around at breaks and try to pair up with her in school. DD was already very insecure that her friend was moving on from the group with her new friends and handled it badly. It was just two pre-teens handling things very badly and navigating life. They had been very involved in each others lives from a young age.
In regards to me saying the other child would not feel left out, I do believe this. She mentally checked out from the primary school group. She now sits on the fence when they suggest meeting up and only does things with them if she is not busy with her new friends. I am happy she is asserting herself and making a new group and have encouraged DD to widen her circle of friends. If DD did not get the part she wanted in the dance show she will be down for a few days and sad, then come back training harder and wanting to improve herself. The other girl does not appear to care. Her own mum says this. She just continued as normal. Its not a criticism, just the truth. She is very confident and does not often dwell on things, she just continues forward. I have seen her shrug off bad test results, not being chosen for things and more over the years.
I do not believe the other parent would purposely plan an event to overshadow DDs but on the other hand I do not know as we have never been in this situation. A lot of the guesswork revolves around how the other child will react. Which I believe she won't actually mind but then will not invite DD back but I do not know.
Finally, yes DD would be crushed. She cannot think that's acceptable to leave someone out then be upset herself but at the end of the day she is 12. These are all very big feelings for her and she is small. I personally think if you do it to other people they have the right to do it back. DD says she would be fine but I know her and I know her reactions to things. She tends to not attach feelings to decisions. Her own or others. So she will do something because she feels it is right. She knows this girl was not very nice therefore the girl should not be invited. I am currently working on this with her but she is 12 and we have never been through this before. She will make a decision without feeling, just based on the facts. The girl shouldn't be invited. She would be fine if its done back as she did it first. She would never expect to be invited back. But she would also not expect her friends to chat about it or the feelings she would have. She is not considering her own feelings or future here. But, as an adult, I can see the bigger picture.
To the person who said I was over invested and anxious - yes I am. I remember being a teenage girl. While I do not think the girls involved here are malicious at all, I simply do not know. The horror stories you hear about bullying are enough to make me very anxious and not want my daughter to rock the boat. But on the other side of the coin not to be a doormat. Which is why I am asking advice from other women who may have had similar experiences. Teenage girls can be vicious. This worries me greatly. I would not go back to being a teenager and navigating life for anything.
I think, at this point, I am going to suggest DD invites all 5 or just the 1 single friend in the group. I feel this will also make waves but is not targeting one person or inviting half of a pair of friends (the core group was 2 x 2 plus 1 single). Thank you all for your advice.