I don't know that I find anything wrong with a coach getting in touch with families of current and very recent gymnasts and just saying they have made the decision to move to gym B. No invitation to come along, no negativity about gym A, no detailed account of how absolutely amazing Gym B is, just a statement about the choice they have made. Parents and gymnasts can take it upon themselves to explore their options and decide what they want to do. The gymnasts and parents will find out eventually, so I'm not sure it really matters who the information comes from. I think it would be a very nice gesture of the departing coach to include something like "Coach Suzy and Coach Bill will continue to work with the team" so the parents/gymnasts don't feel like their whole world is being thrown into chaos and everything is changing, but I also wouldn't expect that.
I don't think it would be appropriate to invite certain (or all) athletes to move with him/her, detailing any problems the coach has with the gym or what caused him/her to leave, explaining why gym B is better (flaunting equipment, cost, or any other major component of the program), or suggesting that moving to Gym B is your child's best chance at meeting her goals. While the coach might have very valid reasons to pass around any of that information, I don't personally thinks it's a great ethical choice. Obviously this is different if there is a major safety issue at a the gym being left.
Honestly, some kids just do better under some coaches. And while a kid shouldn't do gymnastics just for the sake of Coach X, because one day he/she could move across the country, I think in some cases it's okay for a child to follow a coach. Especially if parents have had some issues with the gym leading up to the point and the departure of a great coach is sort of the last straw.