The vast majority of gyms will teach a back walkover before a back handspring. We do, and we wouldn't generally teach a back handspring until the gymnast has a back walkover.
However, the exception is kids with very inflexible shoulders. I find that if a kid is flexible enough to do a back walkover but can't do it, then they are not ready to do a back handspring because there is generally a fear issue about going backwards. However, if they aren't flexible in the shoulders this is usually what is stopping them so I don't make it a prerequisite.
That being said a certain amount of shoulder flexibility is needed to make the back handspring safe and functional, so if there is not enough flexibility here I would not teach a BHS until it improves. Have your DD stand up tall and try to put her arms to her ears while keeping her back perfectly straight. If she has to arch her back to get her arms to her ears then learning the BHS should be put off until the flexibility improves.
That's great that the coaches are now getting more educated on the subject!
In all the years no one ever mentioned to us anything about DD's shoulder flexibility. Not her coaches, not her sports orthopedics doctor when she started having back pain, not multiple PT's (one of them former gymnast). They talked about her hips, her posture, her core, etc., but not shoulders.
Until we went to see Dr. Dave Tilley (the guy who writes http://www.shiftmovementscience.com/ blog), and he told us that DD's shoulders are not flexible enough. Too late at that point, the damage had been done, and she had to quit gymnastics. Makes me wonder if things could have been different if her coaches were more aware of this issue and caught it early enough.