We haven't had similar issues travelling with a small dog in cabin. I always call reservations once the flight is booked and have them add and confirm the pet on there. Then, I always pay for the pet via online check-in without issue. It still requires us to go to the counter to get a boarding pass, though. The only thing I find annoying is that having a pet seems to interfere with the upgrade list/process -- despite the reservation being shown as waitlisted I don't think one actually is on the list.

Sorry to hear you're having such a hard go of it.