Preheat oven to 425. While dough chills, squeeze juice from peach peels and pits into a microwave-proof bowl with rhubarb, thyme, and sugar. Toss peels and pits. Microwave the mixture uncovered for 90 seconds. Stir and microwave for another minute. Add in half the peaches. Set aside and let the fruit macerate for 30 minutes, stirring occasionally, to release the juices. Drain the fruit through a fine mesh strainer capuring the liquid into a large saucepan. Set rhubarb and peaches aside. Add the remaining peaches only to the liquid and cook on medium-high heat until the mixture is thickened and reduced by half. Mash the peaches in the liquid with a fork or vegetable masher. Stir in the remaining fruit. Stir in tapioca until well mixed. Remove thyme sprigs and discard. Let the pie fruit filling cool.
On a very well-floured counter, roll out the dough into a 12-inch circle. Place pie dough/disk into a 9 inch pie plate. I tuck the extra dough under the lip to create an extra thick crust. Cover with plastic and chill for 30 minutes.
Roll out the top dough into another circle and either cut into strips for a lattice or transfer it whole to a parchment-lined baking sheet and chill for 30 minutes as well.
Remove the dough-lined pie plate from the fridge and add in the now cooled rhubarb and peach pie filling. Top with the other disk of pie dough. Trim the edges and crimp the edges to seal. Brush pie with water and sprinkle with remaining 2 tbsp of sugar. Cut 6-8 slits into top of crusts to allow for steam to release.
Place pie on a parchment lined baking sheet and bake for 25- 30 minutes at 425. Reduce heat to 375 and rotate the baking sheet to allow for even browning. Bake another 30-40 minutes. Remove from oven and let cool completely so filling can set up- about 2 1/2 -3 hours. Serve with whipped cream or ice cream.