Thomas,

Unfortunately there is no simple sql that could give you the results you are
after. However this can be done with a bit more complex select:

select
    i.InspectionType,
    i.Inspection_Count,
    Sum(r.ReInspectionCount) As ReInspection_Count
from
    (select
        InspectionType,
        Count(InspectionId) As InspectionCount
    from
        InspectionsTable
    where    Inspector = [Enter Inspector]
     and    InspectionDate    Between [Date From] And [Date To]
    group by
        InspectionType
    ) As i
    left join
    (select
        ii.InspectionType,
        Count(ri.InspectionId) As ReInspectionCount
    from
        InspectionsTable As ii
        inner join
        ReinspectionsTable As ri
            on    ii.InspectionID = ri.InspectionId
    where    i.Inspector = [Enter Inspector]
     and    i.InspectionDate    Between [Date From] And [Date To]
    group by
        ii.InspectionType
    ) As r
        on i.InspectionType = r.InspectionType

I assumed that you are interested in Date Range on original inspections, but
you should be able to easily modify the above to reflect your database
structure and the exact requirements.  please note that the same (or similar)
conditions have to be specified twice - once for inspections count, and
another time - for reinspections count.

If you find that the query takes quite some time to run, consider creating
indexes on InspectionType, Inspector & InspectionDate fields.

HTH