Are these set up as relational records like you have a Family table and a Family Member (People) table?
You need to think carefully through the data structure. As suggested already, you might need a Family table to which individuals are linked.
To get to your actual question about maintaining a count, yes, the Count ( ) fiction serves that purpose. It is the actual data structure that will determine what gets counted to produce the result you want.
Quote from the Wikipedia page:
"The hierarchical database model mandates that each child record has only one parent..."
Ironic example for a family database...
Count ( Field1; field2 ; field3 ...)
Will return the number of non-empty fields from the same record over those so listed.
But as others have suggested, a related table of family members linked to the family record provides more flexibility and count can also be used with that data model to count the number of related records.
I've actually ended up having to set up this data model when recording familial relationships:
Family_Member being a join table so that a single person can be listed as the member of more than one family. This was to reflect the fact that given separation/divorce/remarriage, a single child might need to be listed as the member of multiple families.
Thanks very much, and also for the suggestion.