Você deseja mover a verificação de data para o local da consulta interna.
Tente algo como:
SELECT member.*,card.*
FROM member
LEFT JOIN member_card card on card.member=member.id
WHERE member.id IN (
SELECT DISTINCT m.id FROM Member m
LEFT JOIN Member_Card mc ON (mc.Member = m.id)
WHERE ( m.LastModifiedDate >= sinceDate
OR mc.LastModifiedDate >= sinceDate )
)