I was actually there yesterday with my mom and 2 year old and we made the same miscalculation. Ended up on the pier with GNE first and didn't realize it didn't open until 5 until after my daughter had already picked out with horse she wanted on the carousel. Ended up being fine, just walked down to the middle one anyway.
THIS, however - with all the great pizza at the boardwalk (Mack's, Sam's, Franconi's, etc.), you really chose Dominos? I mean, look, I get how kids can certainly be (and mind you I'm playfully teasing you a bit here), but at some point parents have to prevent them from making terrible, life-altering decisions like eating chain pizza at the Jersey shore.