I have joint custody of my two daughters - the 15 year old…

No, the police will not intervene unless he can get a court order that specifically tells them to do so.

Unless he brings a court application, there would not be any consequences if the children do not go with him. But he could bring such an application, and as I explain below, there is risk to you that the court enforces the order.

He could demand that the 15 year old go with him. If she refuses, he could bring a court application to seek an order that you are in contempt in not allowing the access, and he can then ask the police to assist in enforcing the order. But chances are that if he does that, a court will say that you can't really force a 15 1/2 year old to go, and the court might just say that there will be no court ordered access, and leave it up to her to decide when she sees him.

With an 11 year old, it is much different. The court can and does make orders all the time that require access to take place. The court frequently hears from parents saying that the child is upset or does not want to go, and the court routinely orders that the parent will have to find a way to get the child to go, and will not accept suggestions from a parent that this is impossible. Courts routinely put the blame on a custodial parent if access does not occur in such circumstances, and a contempt finding could be the result. Courts will make orders, albeit very reluctantly, that police will enforce an access order if the parent is not willing to do so.

This is not automatic. If there is significant evidence to indicate why the child is having such strong feelings, such as mistreatment by the father or emotional or psychological issues of the child, then a court might see that it is not in her best interests to force access. That is where the feelings of the older child play a role, as it is a potential sign that there is some larger problem here than just an 11 year old having some spat with her father. In that case, the court will not usually just give up, but would look at whether it is possible through counselling to try and repair that father-child relationship, and can and does order parents and child to attend at counselling sessions if it thinks that may help. But without some clear explanation as to why the child is reacting in such a manner, the court will not let a child of age 11 to frustrate or derail a court order. And without some other explanation of the child's reluctance, the court will have to at least consider that the child is being encouraged to have such displays and reactions by the custodial parent, such as through negative comments by that parent about the access parent.

So if you do not get her to go, the risk is that he brings a court application against you to try to re-establish access, and that a court then agrees that this must occur.