This article is from the Recreational Figure Skating FAQ, by Karen Bryden with numerous contributions by others.
1. Do not become close friends with your or your child's coach and
don't hire a coach who is your friend. If you are in a close
relationship with your or you child's coach it becomes very difficult
to switch coaches or sometimes even talk honestly with them. It is
advisable not to allow your child to spend time with the coach alone
outside scheduled practice. If you find the relationship with the
coach is becoming too intimate, consider a change in coaching.
2. Be respectful to your coach. Be punctual for your lessons and
always pay on time. If you might need to cancel a scheduled lesson,
let your coach as soon as possible.
3. If you decide to take lessons from someone else, it is advisable to
tell your coach upfront, even if the extra lessons will not involve
changes in your regular schedule with your coach. While having more
than one coach is rather common and most coaches will be accommodating
(some will even encourage you and give advice on a suitable
alternative coach to work with), coaches are also human and it may
upset them to find out from a third party.