A family of Microsoft relational database management systems designed for ease of use.
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Sorry this is being such a frustration!
Without knowing what you have tried (the SQL of the query) I can't tell why it isn't working; nor do I know what you did to get a subset, nor why you can't link.
To get the total visits per person you should be able to create a Query based on the Visits table (joined to the Persons table if you want to see the visitor name, as I'm sure you do). Change it to a Totals query by clicking on the Greek Sigma icon (like a sideways M) in the query design ribbon; Group By PersonID and use Count as the totals operator on VisitID. If this isn't working please post the SQL view of your query and indicate in what way it's not working.
Likewise, please describe the subset table (fieldnames, datatypes); how it was created (and why, you should be able to use a select Query to extract a subset without creating a new table); and what happens when you try to establish RI.