This does not see to be serious enough to cause all of this controversy. Family is more important than petty gossip. Who said what to who shouldn't be a reason for a family to be so fractured. I would approach your sister even if it seems useless at times. I would extend my hand for the holidays so that you know you have done your best to make this end. You can't make her forgive her daughter as you can only change yourself. If you extend invitations for the holidays and they don't visit then you know you have tried to make amends. It is up to you whether you will accept her animosity towards your daughter or choose to side on your daughter's position. At some point you have to decide if this pursuit includes siding with your daughter or having family under these circumstances.
If this has been helpful press accept