Is there a way to determine if the attached debugger is a remote debugger?

You can use your own CheckRemoteDebuggerPresent

fromkernel32.dll

From MSDN :

"remote" in CheckRemoteDebuggerPresent does not mean that the debugger is necessarily on another computer; instead, indicates that the debugger is in a separate and parallel process.

You can use it like this:

[DllImport("kernel32.dll", SetLastError = true, ExactSpelling = true)]
static extern bool CheckRemoteDebuggerPresent(IntPtr hProcess, ref bool isDebuggerPresent);

public static void Main()
{
    bool isDebuggerPresent = false;
    CheckRemoteDebuggerPresent(Process.GetCurrentProcess().Handle, ref isDebuggerPresent);

    Console.WriteLine(string.Format("Debugger Attached: {0}", isDebuggerPresent));
    Console.ReadLine();
}