string myString = "WordOne "Word Two"";
var result = myString.Split('"')
.Select((element, index) => index % 2 == 0 // If even index
? element.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries) // Split the item
: new string[] { element }) // Keep the entire item
.SelectMany(element => element).ToList();
Console.WriteLine(result[0]);
Console.WriteLine(result[1]);
Console.ReadKey();