Is not waking up for Qiyam al-Layl before Fajr, despite the mother's attempts, an indication of non-acceptance, and is it considered a sin like intentionally abandoning prayer?

Congratulations on performing the night vigil (Qiyam al-Layl), for it is the practice of the righteous. The time for the Fajr prayer extends until sunrise. If you pray before sunrise, you have performed the prayer on time (ada'an); otherwise, it is a make-up prayer (qada'an). There is no sin upon you if you slept before the prayer time began and woke up after it had passed, for the sleeper is not held accountable, as the Prophet (peace and blessings be upon him) said: "There is no negligence in sleep; rather, negligence is on him who does not pray a prayer until the time for the next prayer comes." Your sleeping through the obligatory prayer is not necessarily a sign that your night vigil is not accepted.