Pretty easy, IMO. Your mom stays behind and you find a new driver and go. First of all, the odds of a baby who is due on 9/14 being born around 8/24 are quite low. Even if that were to happen, it's not the end of the world if you aren't there the moment your brother's baby pops out. It's not you and your wife's baby, it's your brothers. You make the trip to go see him and meet your niece/nephew for sure, but there is no requirement that you HAVE to be there for the hospital delivery moment. Your mom on the other hand does need to be there at that moment as that is her son. If there is any chance she might miss the baby being born if she goes to the game, she needs to stay behind. But you on the other hand absolutely do not; in fact, I would think less of you if you did. So then your only challenge becomes finding a new driver. You either use mom's ticket and accommodations to find another friend or family member who can take mom's spot (personally, I'd offer it for free to someone willing to be the chauffeur), or you start getting a large pile of cash together for a boat load of uber rides. Either way, you 100% go to the game.
Your path is clear, my friend.