In a large pot, add a teaspoon of old bay seasoning and boil the baby yukon potatoes on medium-high heat for 20 minutes. Stir often, and set to the side after the 20 minute mark. You don't want your potatoes to be mushy but you want them to be almost cooked through for the grill.
Preheat the grill to high heat, clean, and then reduce the heat to medium-low. Clean corn and cut kielbasa and set to the side.
Melt 1/2 stick of unsalted butter and combine with 3 teaspoons old bay seasoning.
Place drained potatoes, kielbasa, and corn (layer in this order) in a large bowl. Pour the butter/old bay seasoning mix over the large bowl filled with potatoes, kielbasa, and corn. Mix well to ensure that the butter mixture got on everything.
Place the corn, potatoes, and sausage on the grill (save the butter in the bowl). Close lid and cook for 5 minutes, flip items over and cook for an additional 5 minutes. Add the cleaned shrimp to the butter bowl and toss to coat. Add the shrimp to the grill and cook for an additional 5 minutes. Serve immediately.