Your relationship with your ex is not at all inappropriate, it is highly commendable and ideal for the kids as divorced parents. So what’s your girlfriend’s gripe? Is she jealous or worried you still have feelings for your ex? When anyone gets involved with a divorcee they must understand that the kids come first, and that may mean sharing holidays with the ex. Your situation is atypical but not wrong. Your girlfriend needs to understand somehow that this is a healthy situation. I can understand that it may be hard for her to endure, but she needs to be a grown up and make compromises about this if she wants to be with you. That being said, I don’t have any great suggestions except to explain it to her.