I'm a dance teacher and have teacher certification K-12 and deal with such issues on a regular basis. I always recommend that parents:
1) don't express any anxiety about dropping off, leaving, etc - nor should they overcompensate and over-explain things - a simple "I'll be back when class is over." will work for most. Kids very easily adapt the same behavior as the parents - when they express anxiety and nervousness, so, too, will the kids - they are adept at reading emotions.
2) (most important) - drop off and leave QUICKLY with no drama. The sooner you leave, the quicker they will get to bond and trust the people in charge. The more drawn out the situation becomes, the less likely they will adjust and want to stay for any extracurricular activity. A good teacher/coach will have methods on how to engage and involve the child. And a good teacher/coach will know after the first or 2nd session if something will not work out at all.
In this area, once children have been allowed to get away with "backing out" of something, they will continue to do so because they were successful. They know what buttons to push.
Other suggestions:
* bring a stuffed animal or something to be the audience and watch the class
* sit in the car and leave a cell phone with the person in charge in case of a major disruption - by being out of sight, the child will have no choice but to get used to the leader in charge
Patience is key. If you sense that the teacher/coach can't find a way to encourage, look elsewhere. We have a program for 2 year olds and we have only once in 13 years decided that someone truly wasn't ready for the program. They came back when they were a bit older and were fine. While adjustments of this nature might take 4-5 sessions, follow through is key as you are establishing the atmosphere for future classes/sports, etc. We had a child this fall who was questionable about continuing with the program - probably our most challenging one yet. And we were successful and we made the most progress with her than any other student ever. Patience! Perseverance!
Good Luck!
A.
http://www.danceexpressionsunltd.com/parent_info_guide.htm
http://www.danceexpressionsunltd.com/