I had my DD switch to another gym just 4 weeks ago. Though not a level 9/10, I will share some of the experience.
The decision to leave isn't easy, and I did quite a bit of research on here reading old threads about gym switches. I tend to agree, that if your thinking of a switch you're probably doing it a year late. It's hard, relationships are formed with parents and coaches and between teamates. For us, we made the decision for DD. It was two fold, one I'm in the military and general I work 50+ hours a week plus deployments, so I didn't get to see her much. It was very frustating to know my child was spending more time with her coach than her father. I'm now at a command where my schedule is very flexible and have the opportunity to have quality time with my kids. Second is when DD verbilized what we were seeing. She would have never asked to leave, she loved her teamates and one of her coaches. But once she said what we were seeing, it became a lot easier to move on. Old gym isn't bad, it's competive at L6 and below, there was some coaching issues with inexperience and nepptitism.
We didn't tell them we were contimplating a switch. It was the right move, and I definitly didn't feel as if we owed it to them to tell them up front. After we decided to make the switch, we sent the HC a polite email and thanked him for what he's done with our DD. After that we were instantly treated differently. We asked if DD could come by before or after practice to say goodbye and we were told no, we are the competition now. At first I didn't really understand the attitude, as they often welcome in gymanst from local competitors with arms wide open. What I learned quickly is, for many, not all, this is a business first and relationships come second. In general, I would say hold back the potential gym change info until you know for sure it's happening. I'm sure there are gyms that accept and understand this as part of the process and others, as mentioned above react in a way of offense or to protect there business.
As far as the affect of the switch on DD. I guess it depends on your DD's personality, but for ours, the hard part is one, losing and forming new relationships with coaches and teamates. That is the hardest part for her. I guess the other part is, this new gym, has longer hours and are much more devoted to a strength and conditioning regiment. So, there is a lot more achey muscles. Fortunatly, one of the coaches there was DD's former coach at the old gym, so a bit different than your situation, but it definitly helps that she knows her abilities.
I can say this from experience, if you make the switch and wait to tell them ***HAVE DD BRING HER GEAR HOME*** after her last practice. After we made the switch, my wife went to the gym to collect DD's gear, and was basically treated as if she was going through the TSA at an airport. Litterally followed, after first being refused to be allow her to collect DD's things. It was very strange.