I would think that once the export file is generated, that there isn't much chance that the merge program (i.e. Word in your example) would be able to perform any combining of two or more rows of exported data. 

This might be better handled within Sesame, by modifying your application so that there would be a way to generate a single line in the export file that would contain something like:

1, "Bob", "Joe, Kate"

This would have to be done, I think - BEFORE the export file is generated.  Normally the export file is going to contain a single line per record.

In general terms, this would require that the ClientName record(s) have some way to indicate a specific identity, (be able to differentiate the "Bob's" so that the children get placed with the proper "Bob") and then have some way to concatenate (combine) the data in ChildName for specific "Bob's".

This sounds like a perfect example of a 1-to-many relationship, where you have a single ClientName record for a specific "Bob", and use a Sub-form on the record to contain the possible "many" values which would be the children.

Hope this gives you some help, and maybe some direction in changing your application.