The 121 in year 5 is a bit borderline, and I suspect the panel would like to see something in the mid-120s (to allow for any doubts about how an NFER test in a classroom setting can be compared with the 11+). Having said that, you've a lot of good evidence there, and it is worth appealing. There's also the possibility that the EP report will provide additional support.
the excitement meant she struggled to focus which goes partway to explaining such a lower score. Her HT has said that this demonstrates a degree of immaturity and wouldn't support our case so do we mention it or not?
Well, I would have thought a degree of immaturity is an extenuating circumstance! It's certainly worth at least a brief mention.
The only other thing that was happening at the time was younger DD was having trouble settling into reception class (we have just the two girls) and eldest DD was concerned for her. During a break in the days leading up to the first test she'd taken YDD into library (EDD is school librarian) which was against the rules so she was severely reprimanded and was waiting to see if she was going to lose her position which was quite distressing but I'm not sure whether it's worth mentioning it - as it demonstrates she's not averse to flouting the rules, or whether we can prove it had any bearing on the test.
The panel won't be concerned about any flouting of the rules.
You'll probably be asked exactly when the incident took place, and exactly when the consequences (or lack of them) were known. Obviously you can't prove whether it affected the 11+, but do you have any evidence that the incident occurred, or do you think the school would be willing to confirm it?