You are posting really great questions!
I notice that you are certified by the American Council on Exercise. I found this information in ACE’s second edition of the Group Instructor Manual. Hope this is helpful to you!
Stretches, If Appropriate
“To stretch or not to stretch during the warm-up is a much-debated issue, and there is no consensus in the current scientific literature. ”
The text goes on to say that “instructors are in the best position to know their participants and determine what is best for them. The decision on how to go about warming up and stretching is an individual one. It is definitively known that flexibility is a health-related component of fitness and needs to be included in the workout. Whether it is at the end of the workout, in the middle or during the warm-up should be a choice made by the instructor based on feedback from the participants until more definitive research on the topic has been conducted. It is known that optimum flexibility is achieved at the end of the workout, and dynamic movement should be performed before any static stretching in the warm-up.”
ACE Group Fitness Instructor Manual, second edition pp. 177
Hope this is of help.
To keep stretching safe while participants warm up, I always suggest keeping the stretching ballistic and mild. This allows most to target tight spots without overlengthening muscles that are about to be used, as well as, elevating the heart rate to help acclimatize them into cardiorespiratory activity.
I think it’s been well-established that stretching is most beneficial and productive when done AFTER a workout (or at least when the body’s core temperature is sufficiently elevated). In fact, some studies have shown pre-event stretching can be detrimental to a person’s performance (I’m not sure if this would apply to the average recreational exerciser).
Still, along with a sound warm up (usually a slower, less intense version of the moves in the body of the workout, basically dynamic stretching) joint mobility exercises can be beneficial, as exercises themselves and as preparation for physical activity e.g., shoulder raises/rolls, hip rotation with abduction/adduction (knee up), leg extensions, ankle rolls, etc…
This is a big debate. Some of the major organizations such as ACE and AFAA promote rehearsal movements and dynamic stretching (rhythmic limbering) for a Cardio Warm-Up. Usually short duration static stretches are optional to include and should be performed after the muscles are warm. The research is not 100% at the time. Things to consider as far as including static stretching in the warm up are: type of cardio class, goal of the class and individual, intensity of cardio, type of participants, etc.
I have been teaching for over 25 years and I’m a little old school. I still include some short static stretching (erector spinae, hamstrings, hip flexors, calves) in my all of warm-ups. I includes some static stretching at the end of my post-cardio cool down. I always teach longer duration at the end of the workout.
In my traditional dance and some of my cardio-dance classes, I teach longer static stretching in the warm-up because the workout goal is different from a general population cardio class.
As I can get older and work more with older adults and people with physical disabilities, I believe that flexibility is a very neglected health-related component of physical fitness.