What would you do in this situation?

Ordinarily I would say that if you've made a commitment you should stick to it. However, I believe there are some exceptions to that general rule and this would be one of those exceptions. Since you know his wife can record the games and you know that you won't get to see your niece and nephew very often then I think you should explain the situation to your coach and ask if his wife could record the game this time so you can spend time with family. See if there are maybe some other ways you can help out at a later date to make up for not being able to record the games.