Hi Faithful Witness, DITTO what other posters wrote about just write that you love her or let her go for a few months. IMHO an email with lots of pictures of you and your family having fun and writing wishing you were there would probably have more impact on her. Please remember that she is probably being heavily influenced by her husband.
If your mother still has doubts, help her more than your sister to critically think for herself because it might have a more significant impact.
If you still want to confront your sister, I would recommend writing I love you, she seems more judgemental than when you were growing up, and ask how would she feel if you would stop talking with her for giving you presents just because it is a sunny day. Where in the Bible did Jesus Christ say to shun or not associate with people just because they were tax collectors or Samaritans?
Peace be with you and everyone, who you love,
Robert