That sucks - I wouldn't know what to say except to file a complaint and/or DOT complaint.

I have never checked in two hours in advance for the domestic leg of an international trip, and I've done one a month this year. It's the first I've heard of the requirement and I'd escalate to a supervisor and/or the station manager if they pulled it on me.

FWIW, I've checked in as close as 50 minutes to an international departure and that was with a bag - I was one of the last to check-in, but there was no grief given.

Sorry for the trouble - really not an appropriate way to treat customers.