I think all you can do is attempt to provide a better product than the other gym- coaching, customer service, overall gym atmosphere, getting what you pay for, etc. If people are happy with your product, they'll stay. If they are the type to search for greener pastures and the new gym isn't all it's cracked up to be, they'll return and word will spread around the local gym community. If people are leaving your gym and staying put at the other place, maybe it's time to look at what you're doing and see what the other club might be doing better, or at least what parents seem to be responding to better.
I don't know what kind of experiences this other coach had while working at your gym, but if they were indeed that terrible, maybe she feels she is doing the community a "service" by exposing these things? That would be the best case scenario, though. I know I have had experiences with gyms (not as a coach) that were so incredibly negative that I would advise someone considering that club to steer clear so they wouldn't endure the same experiences I did, and because I know there are better options around.
I think trying to recruit your kids at meets, or anywhere really, isn't really ethical and would raise a red flag. If they are doing that great of a business the kids should be coming to them anyway. I would be upset if a coach did that to my kids, but it's a tough economy and hard to get a new gym up off the ground and thriving, so I guess that's just what she feels she has to do. Just consider it a good time for your gym to think through what it's doing and take the opportunity to make changes. Maybe invite parents to provide feedback, either at a parent meeting or through evaluation forms. Look at the other gym and see what programs they are providing, their prices, hours, equipment, coach qualifications, and "extras"- open gyms, birthday parties, camps, clinics- to see if there is something you are missing.
I think the big thing is communication, talk to team parents, show them you are interested in them and providing them with a product they are happy with. I think some of the biggest complaints of parents leaving a gym relate to inadequate communication.