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Reading your comments it seems you want your daughter happy, wonderful. I possibly get the impression you want her to move but are worried the new gym is not the caliber of the current gym. I think @suebee hit on some valid points. If the elite track gymnasts have a different set of coaches then the track your DD is on and the elite track may never come together. My suggestion is you take her where you think she will be happy and what gym fits her best. You have to decide she is too young to be able to see consequences and how they affect the future. I know it is hard DD changed gyms. The thought of changing kept me awake for months. I knew it was time and it took too long for me to move her. For some perspective, my DD is 11 and doing well but if she were to decide she wanted more if she wanted that elite track I would not hesitate to move her asap.
Oh just for the record I in no way want or think she's on an elite track. !! But if she's going to be spending a billion hours doing a sport she lives I just want to give her the best chance to go as far as she can. I stopped reading when you said elite and had to clarify.