Puppy training classes & too many treats

I am taking my 5-month-old, 7-pound Cavapoo to weekly puppy training classes at PetSmart. I like the training, but find that basically all she does during the hour-long class is eat a bunch of treats. That's apparently how you motivate the dogs to learn. However, it's a lot for her stomach, and she keeps vomiting everything up in the middle of class, and then again after class on the ride home. A woman with a dog of similar size in the class has the same issue. The trainer basically brushes aside our concerns, saying the dogs need to eat the treats to participate in class. Does anyone with a smaller breed puppy have this issue, and if so, any suggestions? I want her to learn, but I don't want a puppy with an upset stomach once a week!