Trying to obtain the intersect of two tsvector values

I have two tables forming a parent-child relationship, in my case a
child entity could appear to have multiple parent records.

Given records of the parent table, I would like to perform a pairwise
determination of shared children between each such pair.

I am thinking of using full text search for this. If this is the right
direction, is there a way to obtain the intersect of two tsvector
values?

Allan.