Isn't YOUR door open to a Christmas visit from her? I would tell her we are eating at X o'clock and she is welcome to join in anytime.. Come by for desert if her schedule don't allow more time or just drop in for a drink/coffee and say "hello"...

I was also politely tell her it is Beanie that I am doing this for. Christmas should be enjoyable for him, not dragging the poor child all over away from his new toys and wearing him out so bad that he is cranky as a old bear all day! As a GRANDMOTHER, she should understand that and want what is best for him!