Network works for UdpNtpClient and WevServer, but not for UdpSendReceiveString

I am in new territory here with the w5100. I am not certain it can be done.

You could try assigning the broadcast address to the shield, but that could potentially cause problems. First of all, you would have no internet connection with the shield. Routers almost always block forward on the broadcast address. It is not valid outside the localnet.