Yes, on a Family Railcard you must have at least one adult and one child using it at all times.
Do you need a child travelling or would a ticket for a phantom child be within the rules (i know you are allowed to use the card with a child under 5 who wouldn't normally need a ticket if you buy that child a child ticket).?
Whats so specially about Long Buckby?
3. Group size: To enable discounted tickets to be used the minimum group is at least one child and one named Railcard holder. The maximum group size is up to four adults (aged 16 years and over) including the named cardholder(s), and four children (aged 5-15 years).
That's from the official terms and condition, suggests you do need a child. Would be silly paying for one when there isn't one, you would pay more than just paying full fare.