It will be ok. I promise. We have switched twice and now we are at our forever gym.
Advice:
1. Do not reach out to the other gym(s) unless you are SURE you are leaving. Anything beyond an anonymous phone call to ask if they will take a new team member is risky. Your current gym will find out if she goes there to be evaluated and they will find out fast. And generally that never ever goes well.
2. Make a clean break. Do not send your daughter to say goodbye. Try to make arrangements for someone to get her
grips, whatever, and bring them to you or you as a parent should go in and get belongings. Have a get together later to say goodbye if you want. Later.
3. Be prepared for some ugliness from old team parents and/or teammates. Sad, but often happens.
4. Be prepared to lose your tuition, any money you've got invested in the old gym.
5. I don't know how old your daughter is, but unless she is an older teen then this must be your choice even if she leaves kicking and screaming. Explain your reasons for why this must happen but make it clear that the decision IS made and you will help her through it, but it is not her choice.
6. Try to meet other parents at new gym right away and try to get involved in carpool, play date, etc with new teammates. You want your daughter to make the new friendships as quickly as possible. If you know someone at the new gym reach out now.
7. Make the announcement to old gym through email. Compliment the old gym and thank them. Unless you are very close personally with old gym nothing good usually comes from in person or phone break ups.
Hope that helps. I'm not sure your reasons for leaving but make sure that you are completely sure that it needs to happen before you start the process. Research THOROUGHLY about the gym(s) you are considering. Get parent opinions if possible and look at their upper optional program. The grass is not always greener and you may need more than one gym switch as your daughter's needs change. Mine did.
Good luck. PM me if you want more info. It will be ok. It felt like dying both times we did it but it does work and the child does adjust!