don't forget as well that your child is a British Citizen, they have to let the child enter ! your wife ?? But they are unlikely to not let the mother in. Getting out could be more troublesome particularly if she has no visa in her passport allowing her entry and exit on residents status to the UK.

A colleague had a Chinese (Citizen) wife and she was allowed to travel between UK and here freely with the child who was British, but then she did have the right of abode in the UK, but her passport was still in her maiden name