I don't know what the grandmother's motive would have been.
Maybe she just didn't want her granddaughter being married to a psychopath, but I'm guessing there's a more devious reason that will be revealed.
No idea if this is related, but granny was talking to Tywin about the "iron bank" earlier at the wedding. That's come up before. I assume it will be significant at some point.
I probably should have guessed that Sansa's necklace had some significance, since that scene where she receives it seemed pretty out of place.