T.-
I can understand your frustration - but I don't think there is a quick fix. Some children just seem to be more sensitive to loud noises and lots of people - they get overwhelmed. I would venture to say that the gymnastics coach caused some damage as far as her willingness to participate. Three year olds need some structure, but we can't expect them to behave perfectly. As far as her finger sucking - that's something that she does to comfort herself and the fact that she was sucking her fingers at the class should lead you to believe she was unsure of the situation and needed comforting - not criticism from her coach - someone she was supposed to trust and feel comfortable with. I believe three is a great age to begin doing some structured classes, but some children probably aren't as ready as others may be. I think that gymnastics coach probably needs to take a class in child development to see that their approach probably isn't the best. It almost makes me mad to read that. It's your job as a parent to help her feel more secure to where she doesn't need the fingers (have you tried a satiny lovey blanket?) not the coach's... We have a gymnastics program for kids at our local church and the coach is wonderful with them. There is some structure, but I say that very loosely. She never forces the kids to do anything and knows the importance of letting them feel secure enough in their environment and selves before moving to "do this like this.."
As for preschool - It would probably benefit her tremendously to attend one. Are your standards something that can be adjusted (like preferring a christian one to secular? - if it was a good one?) I would definitely send her to pre-K because by delaying that kind of thing you may just encourage the problem. Pre-K will give you a good idea if she's ready for kindergarten, though. Dr. Kevin Lehman encourages parents to make the decision whether they think their kids are ready to move on in school. (he's a great parenting resource, look him up). You could discuss this with your dr. but I don't think anything is wrong with your daughter. Some of us are introverts and others extroverts -
As for personal experience - My daughter is opposite, but one of our close friends and playmates fits the way you described your daughter. In my opinion I think it's her mom more than her daughter - as the times she leaves her at moms day out she eventually does fine... (not that you're the one in your situation) But time has really helped in this situation. Since our daughters go to the same class, I always ask the teachers how the other girl is doing because in conversation I hear my friend say how she thinks things are going horribly - when in reality her daughter is actually doing ok. She definitely still asks where her mom is and wants to go home, but with gentle reassurance and redirection from her teachers she makes the adjustment better and better each time.
I'd just encourage you to find the right activity to help your daughter find her confidence in a group setting. Have you considered something like Kindermusik or a moms day out program that is just once a week for a few hours?
Good luck!