I wish I could explain your ex’s behavior for you. I can’t. I can only guess that she hasn’t “moved on” as much as she would like to think she has.
You are confused because she is acting in a confusing way. It might be more helpful for you personally to let her know you are concerned about her and wish things were different and leave it at that. Then take a step back and let her take the lead for now about when and how often you see each other.
Meanwhile — What concerns me the most is that the children are being asked to carry messages. This puts them in an awkward and painful position. They are loyal to you both. They had hopes you would get back together. It’s unfair of their mom to put them in the middle this way and could it may cause them great distress. For that reason, I do suggest that you contact your ex in some way to just remind her that your relationship with your kids is separate from your relationship with her and to please talk, text or email you directly instead of talking to the kids about her feelings about you.
I realize I’m getting this letter weeks after Christmas. I hope things have settled down some by now.
I wish you well.