If it was a one way or return flight I think you would be very safe as I doubt they would turn you away at the airport, you would simply be classed as a no show. In theory the rest of your family could be boarding the plane by the time conformance even spots your a no show. The question would be once you are shown not to be traveling would it trigger any sort of cancellation of the return booking. It is likely that your portion of the ticket would be cancelled but the rest remain, although I am not sure you have grounds for complaint if BA cancelled the entire ticket.