I do hope you get things sorted - what a pity having only 3 choices, and unfair when Birmingham has 6 and Warks 7.
I don't have twins (one at a time was bad enough thank you
) but my ds knows a twin at KECH, whose twin brother attends a different KE Grammar. It seems they have got on OK being separated (one lives down the road to CH , the other has more of a journey) and remain very close, and without meaning to sound harsh, I am sure yours will come through it, particularly if you can someohow get the second twin into KE Handsworth and she will also benefit from a Grammar education.
I also know a family where one twin got BV and the other, Handsworth Grammar (boys). They sent both to Handsworth in the end to be together, although to be honest I wouldn't have done that myself...but then I haven't got twins so can't really judge.
My eldest are pretty close, being exactly 2 years apart. I would love ds2 to get into CH with ds1 not just because of the shared experience, but the obvious practicalities too. But I have to accept that ds2 will get what he gets...I can do my best to support him but if he gets another KE Grammar or Bishop Veseys, I will be very happy for that.
I wish you the best for the appeal. It must have been devastating for the child to miss out questions like that by accident, and could happen to anybody but as you have heard, most appeals are unsuccessful and the best way forward may also be to speak with KenR about getting on the KE Handsworth waiting list asap.