There is cellphone service in the Canyon Village area. There is (limited) cellphone service near (all?) the villages, almost none away. NPS has -NO- plans to allow expansion of cell-phone service.
Wifi is available in Canyon Village Lodge, my understanding is it requires a "pass" from the hotel management.
My further understanding is the band-width is limited. Hopefully the classes are not video, or they may not happen.
The closest Library would probably be in Bozeman. I am also aware of NO "fastfood" or "coffeeshop" offering wifi in the Park.
Due to the distances, don't be surprised if you have to pay for bandwidth.
Personally I would hang the class until you were out of the park.
2008 F350SD V10 with an 2012 Arctic Fox 29-5E
When someone tells you to buy the same rig they own, listen, they might be right. When they tell you to buy a different rig then they own, really pay attention, they probably know something you don't.