Christmas is like a wedding - impossible to complete without grief!
The solutions is the same as well - accept that there will be grief, and act to minimise it.
Why not allocate Christmas dinner to those closest, and arrange for Boxing Day dinner time and night time to two other sets of relatives. Explain to everyone that this is the best and fairesty way to do it, and the stedfastly refuse to be drawn into any arguments / bickering / sniping, and concentrate on enjoying your time at each event.
It is the only way, trust me.