Mozart was already very fluent in verbal Spanish before we arrived in Spain when she was five, but she was not reading in Spanish, though she was an advanced reader in English. She was even beginning to fall behind a bit in her Spanish as her English ( in an all English country) got stronger and stronger. We found out that this is typical for all bilingual kids after about age four as they succumb to the dominant languge ( even when the parents are native speakers of the 2nd language).
Foreign local schools are a fantastic way to become multi-literate and
multilingual while deeply immersing in a culture. it's really been an
awesome experience! In 20-20 hind sight we see it was one of our smartest decisions on our non-stop-almost-8-year world tour. We also spent lots of time in Barcelona with Spanish ( only) speaking friends and all around Spain, so that reinforced the language as well as understanding various accents.
Locals consider her a native speaker, but deep fluency doesn't come quickly and there was a reason we spent those four years and she completed the first 4 grades in Spain. We continue with her Spanish and keeping in touch with Spanish speaking friends even in Asia and as we travel the world. We won't leave Asia until she is reading and writing Mandarin at a 6th grade level.
Not everyone can spend the time that we did ( over 4 years with the school dips) on our world trip, but long term immersion travel can be arranged in various ways for most people who want to make this happen. Some do home exchanges, sometimes just moms and kids go, some dedicate a year and some do it over the summer.