Serial expat here living in country number 8. DD’s home gym is in Hong Kong but she trains in the U.S. and in Germany during summer breaks.
I’ll also assume English is important and start with an overview of options in Asia in case you’re up to a bit more exotic. I’ll leave out the U.K. as it’s already been covered
While Australia would be an option, the difference in levels is important. The poster above mentioned the small number of clubs that would be options. The international school and club circuit in Hong Kong, Singapore, and Thailand (and a handful of clubs in mainland China) use the Australian levels program. The bar skills are nowhere near the level of U.S. bars IMO. Kip to handstand is not even introduced until optionals. For the Asian circuit using the Australia levels program, the number of girls who compete optionals is small and I have not seen truly advanced optionals athletes at the competitions. I’ve never seen an athlete in this circuit do a giant in comp.
In Hong Kong, the only way to access the top level of training is to join the national team and this is only open to HK passport holders. Their new head coach is Russian and many of the other top coaches speak English, so language wouldn’t be an issue but passport would be.
I would generally rule out mainland China for similar reasons to HK and Japan because of language (happy to be told otherwise if this isn’t the case).
Philippines is an interesting option. You can get by using English without an issue. Many coaches come from Philippines to teach h at private clubs in HK. There were also 2 Stanford University athletes who competed for the Philippines in the Olympics this past summer.
Moving westward, the UAE and Dubai in particular are worth mentioning. We briefly toyed with the idea of moving to Dubai last year so I did a lot of research. Many of the gyms follow the US JO DP. The gyms are big, have proper equipment. It looked like many coaches were from Russia/Eastern Europe but I can imagine this will vary from gym to gym.
For some countries in Europe, your fees will be lower because training is done through public clubs as opposed to private clubs. Think your local recreational center. It’s a strange concept coming from the U.S.! This applies to France, Germany, Belgium and I believe the Netherlands as well. Israel follows the same model. For Germany, the websites will be in German, but in our experience many coaches speak English. In Germany they have regional training centres that would be able to coach your daughter. I’ve found that communicating with the club or Verein usually goes a long way. If you are local and pay the fees, you should be ok. The more famous clubs fielding the top athletes at the moment are Stuttgart, Cologne, and Chemnitz. You get a disproportionate number out of Chemnitz but this is because that is the headquarters of the national team. Teenagers move there to train full time. Dusseldorf can also train higher level optionals and trained an athlete from Morocco. I don’t remember if she qualified for the Olympics or not but she did quite well in the Africa circuit.
Good luck and enjoy the adventure!