Melt butter in a saucepan over medium heat. Whisk in half-and-half, milk, and Alfredo sauce mix. Bring to a boil, stirring occasionally. Reduce heat to low; stir in sun-dried tomatoes, mushrooms, and garlic. Cook and stir until flavors combine, about 10 minutes. Cover and keep warm.
Fill a large pot with lightly salted water and bring to a rolling boil. Cook fettuccine until tender yet firm to the bite, about 8 minutes. Drain.
Preheat grill for medium heat and lightly oil the grate.
Toss shrimp with lime juice in a large bowl. Cook on the hot grill until shrimp turn pink and start to blacken, 4 to 5 minutes.
Combine sauce, fettuccine, and shrimp in a large bowl; mix well. Garnish with parsley.