Hopefully it will be teaching the children nothing at all about co-parenting and co-operation because hopefully her children have absolutely no idea that anything is going on at all. Because of course its best to keep children out of the middle of disputes between the parents.
I disagree with that.. once a child is old enough to tell time, that child knows what time they are supposed to shift from one parents home/custody to the other.
If my ex has unforeseeable changes to his schedule, and is picking-up earlier or later, I tell my children because they deal with transition better if they are warned, and they are not standing by the door waiting for him. "Daddy will be picking you up after dinner tonight because his flight is canceled".
However, he might then be booked onto a different flight, and be able to make it on time. "Guess what? Daddy was able to get a different flight and will be here to pick you up for dinner. "
Since he is an effective co-parent, at the time when he thinks he is unable to make it to pick them up on time, he gives me the heads up so I can re-arrange any plans that might be affected. It has happened more than once, he thought he would be delayed and I changed plans to accommodate, but in the end he worked things out, and changed my plans again. It does happen in reverse, but far less frequently .. as I don't travel for work.
When these changes happen, I tell my children "Your dad and I work together as a team on these things". You may argue, but I think its in the best interest of the children to see their parents working together and sharing parenting responsibility despite not being together.