Combine the sugar, water, and peach Jell-O in a large saucepan and boil for 3 minutes. Stir in the peach puree, lime juice, and orange juice. Place in a large Ziploc bag (or a couple of quart-sized Ziploc bags–that’ll be easier to use when you’re ready to make the slush) and freeze overnight or for several days.
When ready to serve, allow the peach mixture to thaw for 15-20 minutes. Combine the peach mixture with the pineapple sherbet and Sprite in a large punch bowl or drink serving container.