How to drain water from a plastic sandbox?
I'd keep it simple. Cut some 2" by 2" holes that wrap from the floor around to the sidewall at the bottom corner, either with a hole saw or jig saw or similar. Use latex-based construction glue or another plastic-friendly adhesive to bond one or more layers of aluminum insect screen over the drain hole from the inside, using a bead around the opening. You could also use pop rivets and washers to secure the screen.

A small amount of sand will work though the screen over time, but it'll mostly stay put. The sand will retain enough water for the kids to play for the short term, but it will drain slowly and keep the box fairly dry.