Although, I know your queries must produce undesired results,
it would save much of my time of guessing and typing and may save some of furthermore dialogue between us,
if you supplied some of your trial queries and the (incorrect) sample output.
Anyway, this may give you some hint.
Code:
SELECT t1.EmpID
, PayEndDate
, BudgetNum
, SUM(Hours) AS hours_sum
, COUNT(t2.EmpID) AS count_t2_rows
FROM TABLE1 t1
, TABLE2 t2
WHERE t1.EmpID = t2.EmpID
AND (predicates for EmpStatus)
AND (predicates for ExpendType)
AND PayEndDate > CURRENT_DATE - (DAYOFYEAR(CURRENT_DATE) - 1) DAYs
AND BudgetNum IN (...)
GROUP BY
t1.EmpID
, PayEndDate
, BudgetNum
;