After processing the watermelon, strawberries, lime juice, and ice, taste before adding sugar; you may not need any. For the star garnish, an adult can press a cookie cutter through the rind with the back of a wooden spoon.
Put watermelon, strawberries, lime juice, ice, and sugar if desired into the pitcher of a blender, and blend for 15 seconds on high speed. (Always put the top on the container before processing.) Stop machine, and stir ingredients with a long wooden spoon. Blend for 15 seconds more on high speed.