I am sure someone will have a better solution, but you could duplicate the entire file and delete all but 10 records and their related records. Then transfer to iOS device.
Or you could export each table of the found set separately in to the appropriate table.
no automatic way to get that. If it's a one time thing, create a clone of the data files, add them to a 'demo' version and create the necessary 10 records manually in the needed tables/files
if it's a regular job the create a demo verison, You could create script for each of the taks, fired from a copy of the original..
If you go with Big Tom's suggestion you could add a cascading delete to your relation and delete all but a few records in your mother table (in the copy) and the children will be deleted.
Alternatively: Go to the main table, find the 10 records you want, go to the empty clone and import those 10 into the same table.
Then in your master file go to related based on found set with "match found set" and now you have all the related children and can import them in your clone.
Not a one click task, but at least not a terribly long procedure either.
tks guys for all your suggestions. I did do as bigtom suggested, as an expedient solution.