Cut the rhubarb into 1-inch pieces and stem and halve the strawberries. Combine the prepared rhubarb, strawberries, and sugar in a large pot with 3 cups of water. Bring to a medium heat and simmer for 10-15 minutes, stirring occasionally, until the fruit is completely soft and breaks apart easily. The rhubarb will release its natural juices and the mixture should look like a loose compote. I like to let this simmer undisturbed for the last few minutes to let the flavors really meld together.

Remove the pot from heat and let the fruit mixture cool to room temperature, about 20-30 minutes. Once cooled, transfer the mixture to a blender and blend until completely smooth, working in batches if needed to avoid overflow. Strain the blended mixture through a fine-mesh sieve into a large bowl to remove any fibrous bits from the rhubarb, pressing gently on the solids with the back of a spoon to extract all the juice. You should have approximately 4-5 cups of smooth, strained fruit puree.

In a large freezer-safe container (at least 4-quart capacity), combine the fruit puree from Step 2 with the apple juice, pink lemonade, rum, and salt. Stir thoroughly until all ingredients are well combined and the salt is completely dissolved. I always taste at this point and adjust the sweetness or tartness if needed—remember that freezing will dull flavors slightly, so don't be shy with adjusting. The base should taste slightly more flavorful than you'd want the final drink, as the ice will dilute it.

Cover the container and place it in the freezer for at least 24 hours. After 24 hours, remove the container and vigorously stir or break up the mixture with a fork or whisk—the goal is to create a slushy texture with fine ice crystals throughout rather than a solid block. Return to the freezer. If you prefer a smoother slush, stir again every 4-6 hours during the freezing process, which will create smaller, more uniform ice crystals. The slush can be stored in the freezer for up to 2 weeks.

When ready to serve, scoop the slush into chilled glasses, filling them about three-quarters full. Top each glass with a splash of lemon-lime soda (about 2-3 ounces per serving) and stir gently to combine. The soda will add freshness and help break up any ice crystals slightly for a more drinkable consistency.