Hi Laura, welcome! :D
Here's the thread on the private lessons cost:
http://www.gymchat.com/messageboards/viewtopic.php?t=203
For vault, maybe by "hands first" your coach means you're not hollow and like are going with your knees or legs or stomach first towards the vault. Also, ask her if the vault board isn't too close to the vault for your height and for your jump and speed - they all
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