Pit fruit, cut into chunks, and put in a large saucepan with 1/2 cup sugar and the lemon juice. Cover, bring to a boil, then reduce heat and simmer until pulp mashes easily with a spoon, 5 to 8 minutes.
Transfer fruit with a slotted spoon to a food processor. Whirl until only tiny pieces of skin remain. Return to liquid in pan, stir in rose water, and chill in a bowl of ice water until very cold, stirring occasionally.
Pour mixture into a 9- by 13-in. pan, cover, and freeze until it's firm but still shows a fingerprint when pressed, about 2 1/2 hours.
Beat cream, remaining 2 tsp. sugar, and the vanilla with a mixer in a medium bowl until thick. Stir frozen mixture to soften slightly, then fold in cream with a few strokes to leave big white streaks. Spoon mixture into 8 or 9 popsicle molds (1/3-cup size) and push a popsicle stick into each.
Freeze creamsicles, covered, until firm, at least 6 1/2 hours. To remove, dip molds in a bowl of warm water about 10 seconds, then gently squeeze pops to loosen.
*Find rose water with baking supplies at well-stocked supermarkets.
Make ahead: Up to 2 weeks.
Note: Nutritional analysis is per creamsicle.