I think all of us face problems with friends and family with eating restrictions of all kinds, whether principled (vegans and vegetarians), allergies or health restrictions.
We have a DGD with allergies to nuts and salmon, both of which foods have been staples in our Christmases. We have decided that the salmon is dispensable, as are a bowl of nuts, I can make my own nut-free puddings, cakes and mincemeat that tastes just the same but when I planned a venison casserole without chestnuts, even DS and DDiL looked horrified. So I made a venison stew, without the chestnuts, then put portion for DGD aside and added mushrooms and added chestnuts to the rest before freezing them.
Much of the Christmas meal vegans and vegetarians can eat: roast potatoes, all the vegetables, stuffing. A Christmas pudding, probably acceptable to all, can be made using veg suet and egg substitute. After that you make accommodation - a nut roast, one portion of vegan 'cheese' and some vegan chocolates.
I would take both children firmly aside before the event and tell the vegan the adaptions you are making and make it clear that her principles are her principles and you will respect them, but she has no right to impose them on other peopel, if she wants to sulk on Christmas day, no one will take any notice of her, then tell her brother that he is not to goad her in any way, in word or deed. Just eat his meat and keep quiet.