In following when talking about 'native speaker' I refer to what is considered as 'mother tongue' rather than reaching a level of fluency.
For the purpose of this question think of an average person who is not a prodigious infant who is talented in learning languages but also not being exceptionally incapable of learning languages. Furthermore, it shouldn't be of interest if languages X and Y are related, say, German and Dutch, or if they are completely different, say, Spanish and Japanese.
As a native speaker of whichever language you are able to recognize other speakers as also being native. When someone learns a language as a second language he'll probably never reach the same level as those who speak that language as first language, even if they live in the foreign country for a long time. There'll (almost 1) always be a few indicator which will distinguish them from native speakers. And I don't refer to accent or similar but only to the language skills and feel for a language, i.e. word-choice, grammar etc.
I was thinking of what would happen if a child is born in country X into a native family of the respective language but being raised in country Y by a family whose native language is Y.
Q1: Will this child ever 'perfectly' speak language Y and be recognized by other speakers of Y as native? Or does this child has an inborn ability to language X and, for that reason, will not be able to speak language Y good enough?
Q2: What would happen if this child will have instructions in their 'inborn' language? Will they easily learn their
second 'inborn' language? Similar, what would happen if this person would move to country X after growing up. Will they be able to learn language X good enough to be recognized as a native speaker of X?
1The exception that proves the rule.