Это будет примерно так:
SELECT SUM(invoice.total_amount)
FROM (SELECT date, total_amount
FROM invoice_main main , invoice_petty_claim petty, invoice_expense_type expense_type
WHERE main.office = 'XXX' and main.id=petty.invoice_id and petty.expense_type = expense_type.type
UNION ALL
SELECT date, total_amount
FROM invoice_main main, invoice_vendors_claim vendor, invoice_expense_type expense_type
WHERE main.office = 'XXX' and main.id=vendor.invoice_id AND vendor.expense_type = expense_type.type
) invoice
GROUP BY invoice.date