I can only comment based on my own experiences to say that for most of the time that we were communicating with my DH's ex, I was the one doing the communicating. I also provided a lot of the transportation, prior to getting an order in place that included transportation. It is not that my DH didn't care, but due to his work schedule and lack of flexibility with his schedule, I was frequently more available to complete these tasks. Also, because of DH's ex's ability to set him off with her attitude and my attention to detail and the children's schedules, it was easier for me to be the primary communicator on our side. There were times when DH did communicate with his ex and he would end up forgetting or miscommunicating details of activities that I would end up having to fix later on. I was also doing my darndest to ensure that my DH was able to see his kids as frequently as possible. Now, granted, this was prior to my younger children being born, but there have still been instances since, where I have done the transportation for some reason or another.
Being as that KH is in the IT field, it is possible that his work schedule did not always accommodate him leaving early on Fridays to take Kyron to meet DY. IT hours can be crazy at times. Maybe he saved the times that he got off early for when Kyron had something special going on, like was the case on that day. Also, it seems that since TMH appeared to be very involved in Kyron's activities, it was easier for her to communicate with DY. It may not necessarily have been a negative thing for her to be the primary communicator and transporter, at least from my experience.