Cut a large orange in half widthwise, then cut off one 1-inch thick slice (peel on) and set it aside.
Squeeze the juice from the remaining orange, measuring out 2 ounces. Set the juice aside.
Add the vodka, peach schnapps, orange juice, and cranberry juice to a shaker with ice.
Shake vigorously for 10 seconds.
Strain the contents through a cocktail strainer into a whiskey tumbler glass filled with fresh ice.
To make an orange twist, take the orange slice you set aside. Cutting carefully with a paring knife, remove the flesh, then cut the peel into a strip. Working carefully to avoid cutting yourself, scrape the pith off the inside of the peel, keeping a thin, mostly orange ribbon.
Twist the peel around a straw and hold it for about 2 minutes to keep its shape.
Garnish the cocktail with the orange twist and two-toned maraschino cherries, then serve.