We are GPs to a 2 yo and 6 month old; last year we bought a portable DVD player for the plane ride and beach time for the 2 yo when he was 12 months.
Also, a cotton sheet is good to have for them to nap on the beach under a palapa. EZ to shake, wash, & dry each night for next day use.
Foldable beverage bags (large w/compartments & /zip lock bags for snacks & for holding ice (re-freeze em overnight to save water)
Sunscreen is a MUST! Plus UV resist. shirts; we bought the long sleeve shirts for the boy so he could lay in his little floater with us. Brands such as; http://www.solartex.com/
I use long VELCROŽ strips to secure zippered beach bags to the chairs.
Wally Mart, etc. sells an assortment of rolls in various bright colors for a ~$4.00 a box. It helps stop and grab-and-go folks and is relatively EZ to use for other uses such as securing rolled beach towels and bundling up the kids beach toys. Grand children girls like em to make bracelets...lol