I send mail by using sendmail from a command line. I have to relay through gmail to get through (my computer's domain is a fiction). Today a message was returned because Barracuda Central identified on account of the sending domain's reputation. The sending domain was the city government's. (I sent from the library, using its WiFi). I thought the message went through gmail, thus would seem to have been sent by it. I must misunderstand. If I try to send a message directly from my domain nobody accepts them.

http://www.barracudanetworks.com/rep...16.234.200.179

I suggest you send yourself an email to an address that is yours but not a gmail address.
Check for that email and if you get it then have a good look at the headers - (most email clients will allow you to see the headers)
You will see the entire 'trail' from source to destination outlined in the header.

There really is no easy answer to what you are asking. That wifi connection may allow connections to its email server, and it may have gone out the governments server as you say, or maybe not.

Check the headers. Post them here after sanitizing them, maybe we all can figure it out

FWIW my request for re-classification (even though I'm just a citizen) worked *and* the target of the message responded.

gmail keeps sent messages in the 'sent mail' file; I see no sign of my Albuquerque's domain in the header. I've sent messages to myself to see what they look like before.