For up to 3 accidents total, it's relatively straightforward, with a single table pass for each table -- afaik, beyond 3 would require additional code/complexity (at least one additional join/select back to #tblDrivers).

SELECT

d.DriverID,

MAX(d.FirstAccidentDate) AS FirstAccidentDate,

MIN(CASE WHEN ds.ClassDate >= d.FirstAccidentDate THEN ds.ClassDate END) AS DrivingSchoolDate,

MAX(d.SecondAccidentDate) AS SecondAccidentDate,

MAX(d.ThirdAccidentDate) AS ThirdAccidentDate

FROM (

SELECT

DriverID,

MAX(FirstAccidentDate) AS FirstAccidentDate,

CASE WHEN MAX(AccidentCount) = 1 THEN NULL

WHEN MAX(AccidentCount) = 2 THEN MAX(LastAccidentDate)

WHEN MAX(AccidentCount) = 3 THEN MAX(MiddleAccidentDate)

ELSE NULL END AS SecondAccidentDate,

CASE WHEN MAX(AccidentCount) = 1 THEN NULL

WHEN MAX(AccidentCount) = 2 THEN NULL

WHEN MAX(AccidentCount) = 3 THEN MAX(LastAccidentDate)

ELSE NULL END AS ThirdAccidentDate

FROM (

SELECT DriverID,

MIN(AccidentDate) AS FirstAccidentDate,

CAST(DATEADD(DAY, 0, SUM(DATEDIFF(DAY, 0, AccidentDate)) - DATEDIFF(DAY, 0, MIN(AccidentDate)) - DATEDIFF(DAY, 0, MAX(AccidentDate))) AS date) AS MiddleAccidentDate,

MAX(AccidentDate) AS LastAccidentDate,

COUNT(*) AS AccidentCount

FROM #tblDrivers

GROUP BY DriverID

) AS d2

GROUP BY DriverID

) AS d

LEFT OUTER JOIN #tblDrivingSchool ds ON ds.DriverID = d.DriverID

GROUP BY d.DriverID

Edit: Refined the SQL code slightly.