Does the family's discovery of the sin after repentance indicate its non-acceptance, and is repentance from a major sin accepted?

Repentance from all sins is accepted if its conditions are met: remorse, cessation, and determination not to return to the sin. Someone knowing about your sin does not affect the validity of your repentance; rather, it might be a test of your sincerity. Continue your repentance and do not worry about anyone knowing, and remember that the one who repents from a sin is like one who has no sin. Allah accepts repentance from His servants and forgives all sins, as He states: ﴿Say, "O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful."﴾ [Az-Zumar: 53].