Twins are discussed in the Q&As. (B24)
There are two separate issues: non-qualification, and then oversubscription. (As places are offered by rank order, I'll assume there are no vacancies.)
Is there any mileage in highlighting the emotional pressure (and subsequent depression) of having a brother who excels so in the 11+ subjects?
Yes, sibling rivalry is an extenuating circumstance.
Are the panel allowed to make reference to the travel arrangements and social/emotional impact of separating twins who have always attended school together?
For oversubscription, yes, but it doesn't really apply to non-qualification.
If daughter does not get her GS place then she will be home alone in a remote rural area every day - having walked along a mile long unlit, pavementless country lane from the bus stop to home - will this affect their decision?
Not for non-qualification, I would have thought.
Appeals are basically the same everywhere (because of the code of practice), but the way in which they are organised varies, and, in particular, the success rate varies dramatically.
As you are talking about an own-admission authority school in an area where there aren't many grammar schools, I assume they will deal with non-qualification and oversubscription at the same time. (See the "Lincolnshire model" in the Q&As, section E.)
The success rate for appeals at own-admission authority schools is usually below average, I'm afraid.