I would email her with "Sorry, we won't be able to attend after all. Hope you have a great party."
Why? 1. You don't know cousin and uncle that well. 2. The party is 4 hours away, one way. That is an 8-hour round trip at the least. 3. The invitation you were originally given has changed.
If the party had been presented to you as a mini family reunion, lets all chip in on the food for x and y meals, we will do the birthday dinner meal, etc., it would be entirely different. But to have it changed at the last moment, no just no.
Cancel and enjoy the time off with your immediate family. Or cancel your days off and use them later on for something fun.