Do we know what language Hoshi was teaching during Broken Bow?? Most obvious answer is Vulcan but it doesn't sound very Vulcany..
I don't believe it was ever stated what language she was teaching, but it's fun to speculate! My pick would be Draylaxian. In 2151, there wouldn't be that many species humanity had come in contact with, and certainly very few that are in regular enough contact to warrant a language course being set up. Except for a few visitors via Vulcan programs such as the Interspecies Medical Exchange, it was probably the Earth Cargo Service that had the greatest amount of alien contact. Denobulan doesn't seem to feature those trilling sounds, and as you say, it doesn't sound very Vulcan either. So my guess is Draylaxian, since the ECS set up a regular trade route with them.
Just checked with Diane Carey’s novelization of the pilot and she has it as an alien language. No idea if she’s just extrapolating that on her own or if that’s info she somehow got from the script writers, though. I guess both would make about equal sense; she could be teaching an alien language or an Earth language. But since they’re establishing her as a xenolingust/exolingust, it probably was meant to be an alien language, yeah. Plus, the actual words she’s using in the episode don’t seem to correspond to any actual Earth language.