I don't get why there's so much pressure for you to be at the hospital anyways. It's not your kid, it's not your grandkid, it's your sister's kid. The hospital time itself is pretty much miserable for everyone involved. It's not until the new parents and the newborn get home that anyone can start really enjoying the moment anyways. It's ridiculous, IMO, that you'd be under any pressure to be at the hospital itself. You go in relatively short order after word the baby has arrived, visit your sis, see how you can help out the overwhelmed new parents, and meet your niece/nephew. That's your role and obligation. Anything beyond this is overly demanding and 100% based on emotion and not rational thinking.
Your mother is a different story though. So ultimately the question you need to be chewing on isn't if YOU must stay home from the opening game for the very small chance she might deliver that weekend just so you can claim later you were at the hospital... this analysis should solely be whether you can find someone else other than your mom who can drive and help out with your needs. If you can, you go for 100%. Even on the very slight chance that baby comes out 8/24 or 8/25, no big deal, nothing lost, you go visit your sister Sunday night or Monday morning. Same sh-it other than this silly emotional-based principle that people can say you were at the hospital.