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Contar registros de dos tablas agrupadas por un campo

Parece que estás tratando de hacer esto:

select d.RepName, count(d.RepName) DoctorReportsCount, count(h.RepName) HospitalsReportsCount, d.DateAdded from doctorreports d inner join hospitals h on d.RepName = h.RepName group by d.RepName, d.DateAdded

editar:

select * from ( select d.RepName, count(d.RepName) DoctorReportsCount , d.dateadded from doctorreports d group by d.RepName, d.dateadded ) d left join ( select h.RepName, count(h.RepName) HospitalsReportsCount , h.dateadded hDateadded from hospitals h group by h.RepName, h.dateadded )h on d.RepName = h.RepName

ver SQL Fiddle con demostración

edición n.º 2, si desea devolver los datos de los días que faltan, le recomendaría crear una tabla que contenga las fechas del calendario, luego puede devolver los datos de los días que faltan. Lo siguiente debería devolver lo que está buscando. Tenga en cuenta que creé una tabla de calendario para esta consulta:

select COALESCE(d.drep, '') repname,
  COALESCE(d.DCount, 0) DoctorReportsCount,
  COALESCE(h.HCount, 0) HospitalsReportsCount,
  c.dt Dateadded
from calendar c
left join
(
  select repname drep,
    count(repname) DCount,
    dateadded ddate
  from doctorreports
  group by repname, dateadded
) d
  on c.dt = d.ddate
left join
(
  select repname hrep,
    count(repname) HCount,
    dateadded hdate
  from hospitals
  group by repname, dateadded
) h
  on c.dt = h.hdate
  and d.drep = h.hrep

ver SQL Fiddle con demostración

Si no te importan las otras fechas, así es como lo harías sin una date tabla:

select COALESCE(d.RepName, '') repname,
  COALESCE(d.DoctorReportsCount, 0) DoctorReportsCount,
  COALESCE(h.HospitalsReportsCount, 0) HospitalsReportsCount,
  COALESCE(p.PharmacyReportsCount, 0) PharmacyReportsCount,
  d.dateadded Dateadded
from
(
  select d.RepName,
      count(d.RepName) DoctorReportsCount
    , d.dateadded
  from doctorreports d
  group by d.RepName, d.dateadded
) d
left join
(
  select h.RepName,
    count(h.RepName) HospitalsReportsCount
  , h.dateadded hDateadded
  from hospitals h
  group by h.RepName, h.dateadded
)h
  on d.RepName = h.RepName
  and d.dateadded = h.hDateadded
left join
(
  select p.RepName,
    count(p.RepName) PharmacyReportsCount
  , p.dateadded hDateadded
  from PharmacyReports p
  group by p.RepName, p.dateadded
)p
  on d.RepName = p.RepName
  and d.dateadded = p.hDateadded

ver SQL Fiddle con demostración