Good grief. Our older daughter is Down Syndrome. We came here when she was eight. She had been in an integrated class in the UK. Here she was shoved into speech therapy, still is at 13, because she has difficulty with some sounds. We were 'advised' to only speak French with her at home, not have UK TV and so on. However, in four years at primary (she was extended one year) she was no further on in any respect than when we came. However, by then she was bilingual. Her mother's first language is Italian, although she is now multi-lingual, and I am bilingual with other language skills. So our younger daughter has at least a smattering of several. In that respect, our children are allowed to take their own course with language. We even explained that rather than teach them our languages we let they pick up what they can. We had lots of speeches about that being pedagogically wrong, they must concentrate on French and avoid other languages that would distract.
Our younger daughter was always in the top three in her class in primary, but never the top in English as they expected. She was simply too far ahead of the class, yet nobody advised she stop using English any longer. But then she was fluent in French in two years and wrote it as well as speaking it by then. She is now learning German at college. She has learned some spoken German from me but not reading and writing. One she had got used to accented letters in the German she proclaimed that reading is just like speaking when you know the letters. I guess it is true, I had never thought about it.
One year and a bit at college, albeit in a ULIS, our older daughter now reads, slowly but well enough, moreover understands what she reads. She also recently got 19.5 out of 20 for English and was so proud of herself. The younger is now at college and in this first term has discovered diversity and is now racing on.
Just this evening whilst 'stealing' a piece of cheese as we prepared dinner, she read the wrapper. Pecorino romano. She read it with an Italian 'pronunciation' and then said to me that it is Italiano. When she goes on family visits she understands if not says much, but then my Italian is only minimally better. The psychologist and speech therapist were both at one of the parent school meetings last year and making those disapproving sucking in of air noises when we made example of her being technically trilingual. We had been told 100% certainly she would never be bilingual.
I could ramble on. It is a farce at times. They tell us what we should do and not do, we do pretty well the opposite in most cases. We are both professionals who study children, not educationally and not linguistically, but I have pushing 45 years of work directly with children and youth and two generations of my own bilingual children behind me. Tell them that and they will say "Ah, but...".
So, kind of leaning toward what Kathrin, Debra and Christine are saying, it is probably most important that you a) follow your children's own instincts, b) let your own instincts follow theirs, c) ignore most of what teachers tell you and d) help them maintain their bilingualism as an asset for the future.