Although it is hard to imagine your "little" girls travelling to big school on their own, you also have to be realistic and realise that they grow up very fast and, for most children, the journey to and from school is one of the highlights of the day. And, as Eccentric says, up to now, most brighter end children have always succeeded - the later you come to your first "failure" the harder it is to cope with it, but sometimes you just have to.
This is going to sound harsh but, your daughter is coming across a little bit as if she has a sense of entitlement to a place - you have to explain to her that she doesn't - yes she passed but, unfortunately, lots of other children passed with a higher score and the school only has a certain number of seats. Twin 1 was one of the ones who has been allocated a seat by right and twin 2 should be pleased for her, even if she is disappointed for herself. It is not Twin 1's fault that she scored higher. I think you need to explain to Twin 1 too that she will not have to give her place up (very late in the year) if Twin 2 does not win her appeal in June - if Twin 2 is saying this openly to teachers at school, you can bet your bottom dollar that Twin 1 has heard it and the fact that she is now talking about school bag choices etc, she is trying to force the issue - start buying things for my GS school, mum, and make it real so that you don't then snatch the place away from me in June if it doesn't happen. You need to reassure Twin 1 so she is less likely to then feel angry at Twin 2 for "losing" her her place as well and more likely to be a bit more sympathetic to the nerves Twin 2 is feeling.
Any appeal has a chance of success and a chance of failure - you need to focus on Twin 2s ability and why this particular school will be the best fit for her - part of that argument will be that she has a twin there - although, I have to be honest, from what you are saying about her reaction, I wonder if they both might benefit from being able to blossom in different schools and be successful in their own rights, without the constant comparisons that they obviously make of themselves, let alone staff and other children make!
However you have a relatively strong case but - and this is a big but - you and your husband need to make concerted effort not to let your angst rub off on her - stopping talking when she comes in the room is tough at any age, as you immediately believe people are talking about you! I'm sorry if this all sounds harsh but I do believe if you focus on the academic ability and best fit and then the added confusion of the m/b policy you may have a strong case.