As someone that was raised bilingual I can guarantee you that what you described is usually a self made problem.
Learning a language strictly in school while speaking your native language at home is only a detriment when children don't get to interact with others after school.
So unless they spend all of their time after school at home only interacting with people in their native language the exposure to both languages should be more than enough to get a child fluent in both languages by the time they finish school.

Being fluent in a language does not require you to know it's grammatical rules. Most native speakers just subconsciously know how to form proper sentences trough enough exposure to the language.