If your presence at your nephew's birthday party is so important that you not being there will ruin his party, then you should have been told about the party a few weeks ago. Do not go to the party. Do mail the card and/or gift to your nephew (everyone, no matter how young or old, loves to get something special in the mail), do call him on his birthday and wish him a happy birthday, do not go to the party.
Oh, and I would also tell your SIL that the reminder she sent out was not a reminder for you, as you hadn't been told about the party before, so therefore, this was your first notification. It could be the SIL asked MIL to tell you and MIL is the guilty one here; it could she mailed you an invitation and your post office is the guilty one here; it could be your email server sent the original invite to spam - but you didn't hear in enough time and you have plans.
Also, I couldn't tell from your post if going to the party would mean cancelling the plans you've made with other people, but if that is the case, to do so would make you ruder than your SIL - you aren't cancelling for an emergency, you are doing so because they aren't as important to you as your SIL and her son.