Excellent, intelligent posts from TamIAm on this thread.
At the end of the day, a 6 year old does have a right to choose to not be in a photo. It's highly likely that the grandmother has other photos of the child anyway, and if it's really important to her to have a photo with all of the grandchildren in it, then I still think photoshopping is the answer. The grandmother knows all the children were there for Christmas, the memories are there, but if this group photo was the be-all and end-all then just photoshop it.
However, one thing that doesn't add up for me is that the OP says she 'can't stress enough the importance to the grandmother of having the photo ' - yet the decision to take the photo was taken just 5 minutes before the brother had to leave!! Surely if it was so important this would have been discussed earlier? I also think a far better option would have been to present granny with a book of naturalistic photos just snapped throughout the day.
The thing that strikes me most though is the fact that the grandmother was terribly upset by having a photo with one grandchild not there. The grandmother is the adult and should be able to deal with it without feeling desperately disappointed. No adult should rely on a child complying with having their photo taken for happiness. It's just wrong. One of my children really dislikes having their photo taken, as a result we have fewer photos of this child than the other, but the ones we do have are lovely natural photos which were not a cause of stress or upset. Many adults dislike having their photo taken too. No one would dream of forcing an adult so why try to force a child?
At the end of the day, the child was not hurting anyone else, or behaving in a way which needed to be stopped. Sure, she may have been in a huff, but the op does not say that this was spoiling the day for everyone. It sounds as though ignoring and not rising to the behaviour was exactly the right response. Adults are more likely to encourage children to behave in positive social ways by modelling the behaviour they want. Certainly not by forcing the child to do something arbitrary like being in a group photo. If the child had been rude to an adult, or hurt another child, or snatched someone elses present - sure, absolutely, deal with it. But not participating in a group photo is not hurtful to others. This situation reminds me of ones where I've been in where adults have tried to make all the children join in a particular game (another bane of many family christmases). It's about the adults gratification rather than respecting that children dont have to participate in everything