Do not attempt to remind her of what she had and has lost. Right now, she is living in her present and has blocked most of the good things from the past w/you and your family.
I wouldn't send her a meaningful gift. If you get anything, make it impersonal and from the children. Right now, she is in a dark place and nothing is bright and airy for her when it comes to you and the relationship.
Oh, those words about you haven't changed or nothing has changed...they are the words of someone who is looking for something to make them feel better. They don't have a clue as to why they feel the way they do, but they think that if everyone and everything would change, she would feel better. That is a bunch of BS. She is definitely looking for something to make her feel better about herself and her little world. Unfortunately, she doesn't realize that the only way to make herself happy is to look within. Exterior things will only bring you joy for a bit and then...poof! Then you look for something else.
Only communicate with her about the children and Christmas visitation. Leave the relationship talks alone. The more you attempt to show her what she had and what life can be at the moment, the more she's going to pull away. Keep the focus on you and your children. Leave her be. Always remember, actions speak louder than words. Show her that you can move forward and have a fulfilling life w/o her. Show her the man you were when you met.
Dig deeper for patience and just leave her be.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.