As a single mum of a sporty 15DS, I can see it from your ex's perspective. I am assuming DC is a boy? At that age, boys want their dad to attend their sporting events because that's the time they feel they bond best with them. DS stopped contact with is dad last year and the fact that he showed no interest in his school and sport life was one of the reason.
I take DS and you can see the difference between the kids who come with their dad and those who don't. Out of 5 boys, 3 have separated dads, and all three don't bother to come whereas the others come with their dad who are fully involved with the team.
It sounds like there are two issues in your case, firstly a lack of clear organisation. It sounds like you need better communication with your DC so you know what is happening in their lives and their intentions/plans don't come as a surprise.
You then need to decide how you allocate your time. As already said, when kids do sport, your week-end life is messed up. DS had training football training yesterday and they were still not sure whether the game due to take place this morning, 1 hour away would happen or not or at what time. Got a call last night to say the game was on, needed to meet at 8:15, ready to travel for a start game at 10. That would have mean not being back before 1pm. Got up, went there, stood for 20 minutes in the cold to be told the other team had cancelled the game.
If you want closeness with your teenager, you'll need to be involved in these days. Your wife is being unreasonable to expect the entire Saturday dedicated to her. How old she is! Firstly she's got you all over time, even if you are busy during the week, and secondly, she'll have you for herself for many years to come in only a few years.