There is a name for what he is doing. Parental Alienation. I missed that, and I saw the aftermath of it with my niece and nephew. It took my sister pointing it out. Her children are still in therapy as a result. He is not saying anything negative in front of them, but he is showing zero empathy and does not have a care in the world for the other parent. The characteristics are there. She wants to spend time with them, and he shuts it down, thereby alienating her. In time, they will turn against her, resent her, and reject her as a whole.
Right now, it is the behaviours of it, but prolonged exposure can cause PAS or Parental Alienation Syndrome. There are three stages of PA/PAS. My niece and nephew were in the advanced stage, which is stage three. Their father filled their head with lies and sent my niece back with a "mission" that we found when we searched her things. Mind you, they were 9 and 7 at the time this happened. He had my niece recording conversations for him, spying, and she was a disrespectful little something.
Matt's behaviour coincides with a mixture of stage one and two. He does not care that they might want to see Si or vice versa. He distracts by doing something with them, so the thought to see her is forgotten in that moment. He avoids places where Si might be if he is out with our children. He is not trying to facilitate any communication between our children and Si. He does not even extend the offer for them to call her or anything. He is refusing to communicate with her beyond the scope of saying "no" when she asks to see them. He is not at the point where he is passing messages through our children because they have minimal contact as it stands. He is keeping her away from him. Before it was, she can see them, but not in the house because she is welcome here. If he is somewhere with our daughter like at a class, Si is not welcome to be there at the same time.
It is going to take a meeting with Parental Alienation Consultant for him to see what he is doing. While they will resent her now, when they get older and understand it, all hell will break loose. The problem with getting him to see this is he does not see her as a parent. It is going to take a professional who he is equipped to handle this. A mediator is not good enough.
At least now, I have an idea of what it is, who needs to get involved, and I cannot thank my sister enough for pointing this out.