Over the years my children have started various new jobs, and they've often had other commitments already scheduled by the time they started, in one case my son had a 10 day vacation to Japan planned. Part of the hiring process included my various children telling the prospective/new employer that they had a prior commitment on X day, and in no case was that a deal breaker.
I don't know what position you're applying for, but I see no reason not to just tell your employer that you have a previous commitment for that day, and see what happens. You'll either be told outright that it's a deal breaker, in which case you have a decision to make...or they will accommodate you, and over time you can display an exemplary work ethic so that you'll be able to dispel any initial unfavorable impression they have of you.
If you don't want to run the rest of rocking the boat at all, then you'll have to renegon your agreement to watch your grand.