If the child knows they can speak in either language to the nanny, mum, etc, they'll default to the dominant one. That's why it's important there is clear boundary as to which person speaks each language.
I grew up trilingual and the minority language was only spoken at home. My parents were very strict about not allowing us to use the dominant languages when talking to them, even though they were both perfectly fluent in them, and is what they spoke at work, in the shops, when dealing with our schools... Even outside the home, unless having a conversation with someone else, we had to speak a specific language in the family. Of course as we got older things changed, between the siblings we very rarely spoke that language to each other, once we started school.
Most of my social circle is raising bi/trilingual kids, and from observing both their children, and remembering friends of my parents who were in the same situation as us growing up, it's definitely worth it being very strict on this. The minority language will get lost, accent muddled up, unless kids know they're expected to use it exclusively with certain people. It's not confusing at all, because kids are clever and able to understand that 'mummy speaks both French and English but I only speak French with her, and we speak English when we see my school teachers, or when we go shopping together'.