For the vinaigrette: Pour ½ cup of the olive oil into a glass measuring cup or small bowl. Add the mustard, vinegar, lemon juice, lemon zest, garlic, shallot, 1 T. dill, ½ tsp. salt, and ¼ tsp. pepper. Whisk together vigorously until the vinaigrette combines and thickens.
For the rice: Stir the rice, chicken stock, and remaining salt and pepper together in a medium saucepan. Bring the mixture to a boil, cover, reduce heat, and let simmer – stirring occasionally – for 15-20 minutes until all the liquid is absorbed. Remove the rice from the heat, let it stand for 5 minutes, and then stir in the parsley, remaining dill, and ½ cup of the prepared vinaigrette.
For the seafood: Pat the shrimp and scallops dry with paper towels, and season with salt and pepper. Heat the butter and remaining 1 T. olive oil in a large sauté pan over medium heat. Add the scallops to the hot pan. Sear the first side for 3 minutes, flip, and cook for another 2 minutes on the other side. Remove the scallops with a slotted spoon and place on a plate.
Add the shrimp to the pan and cook the same way (sear the first side for 3 minutes, flip, and cook for another 2 minutes on the other side). Add the scallops and their juices back into the pan with the shrimp, pour in 1 T. of the vinaigrette, and cook for just 1 minute longer to coat the seafood in the sauce.
To serve, place the rice on a plate, top with scallops and shrimp. Garnish with lemon slices and drizzle more vinaigrette on top, if desired.