Mary,
First; A warm welcome to the Forum and SBs.
This site involves real scholarship as far as they make 'em.
Ref: Dental Emergency;
First, do factor in to this prep that in disaster events, much of emergency dentistry involves the closely-related head trauma.
Yes, dental emergency classes do exist. As for "non-professionals", we all have too many different definitions so difficult to clearly address this question on classes.
I'm a non-health care volunteer with Virginia Dental Association working the emergency pop-up dental clinics ... mostly in Appalachia. I learn much over meals with dentists at the motels' breakfasts and expresso breaks.
I've taken 4 dental school classes for emergency field dentistry. It was suggested that if I wanted to get more dental education go to the closest community college and ask about the program "dental assistant". This is not the hygienist program but a little-used program involving how to work the X-ray machine, the dental adhesives and how to make them, the RX pharma for infection control, pain-killers, and the etc helping a dentist.
In non-chron order;
Get all the pubs mentioned here on thread involved the theme "When There's No Dentist ...".
To dental emergency kit, consider adding a magnifying mirror and a ~ 6 X magnifying glass along with a quality clamp-on anywhere good battery-powered light. Also have a "pen light" avail.
Since you mentioned - sutures - , note that here with pop-up emergency clinic program, was taught that most dentists choice braided nylon sutures for procedures not requiring a dissolable suture.
Again, a warm welcome to the Forum and subject-matter boards.
Transmitting from coastal Virginia.