I'd make the .dll into a .exe. If you have the source code for the .dll file, then you can modify the project output on the project properties page to output an executable binary. If you don't have the source code, then you can create a new project that builds to a .exe. The new project should reference and invoke the .dll file.
To launch the .exe from your C# application (assuming the .exe is in the same place as your main application .exe), call Process.Start as follows:
Process.Start("MyOtherApplication.exe", "arg0 arg1 arg2");
This will start the application as a completely separate windows process. So killing your first application will have no effect on the second one.
@Matthias suggested launching the other application using the new operator. If you wanted the two applications to have the same lifetime, and perhaps share memory, then this may be appropriate.