OK, critical question:  For a given activity, will there be one and only one datePerformed value in the table?  Based on your description, I'm guessing that is the case.  But, the solution depends very much on whether that is absolutely true.

How are table1 and table2 linked?

When you retrieve the data from the database, what does a typical record look like?

For a given "The ActivityName1" how do I know what "The ActivityName2" is going to be? 

If I am thinking about this correctly, it is not going to be a simple solution.  You are going to have much better luck doing this in SQL, with a somewhat sophisticated self-join of the inner join result. 

OK, let's take a shot at this.  I'm going to assume, for the sake of this, that all you need is the date.  If you need other information from the record with the latest date, it gets a little trickier.

There are a couple different approaches. 

SELECT tblStart.datePerf AS StartDate,
    tblEnd.datePerf AS EndDate,
    DateDiff(d, tblStart.datePerf, tblEnd.datePerf) AS DaysOpen
FROM
    (SELECT Max(table1.datePerformed) AS datePerf
      FROM table1
      JOIN table2
      ON table1.PrimaryKey = table2.ForeignKey
      WHERE table2.activityPerformed = 'The ActivityName1') tblStart
JOIN
    (SELECT Max(table1.datePerformed) AS datePerf

      FROM table1

      JOIN table2

      ON table1.PrimaryKey = table2.ForeignKey

      WHERE table2.activityPerformed = 'The ActivityName2') tblEnd

This method figures the maximum values for each date in separate subqueries, performs a cross product (since there's only one record in each result, this is pretty trivial), and takes the result.

SELECT
    MAX(CASE table2.activityPerformed WHEN 'The ActivityName1'
            THEN table1.datePerformed ELSE '01/01/1970' END) AS StartDate,
    MAX(CASE table2.activityPerformed WHEN 'The ActivityName2'

            THEN table1.datePerformed ELSE '01/01/1970' END) AS EndDate,
    DATEDIFF(d,
            MAX(CASE table2.activityPerformed WHEN 'The ActivityName1'

                    THEN table1.datePerformed ELSE '01/01/1970' END),
            MAX(CASE table2.activityPerformed WHEN 'The ActivityName2'

                    THEN table1.datePerformed ELSE '01/01/1970' END)) AS DaysOpen
FROM table1
JOIN table2
ON table1.PrimaryKey = table2.ForeignKey

This method is much better if you do want to get additional information out.  But, the CASE construction can be tricky, and it's easy for bugs to sneak in.

You can put it in a SQL Command object (found in the Data tab under the currently open connection node).