Which is better: Tahajjud and Fajr prayers followed by a short sleep, or Fajr prayer and reciting a portion of the Qur'an, knowing that sleep is necessary either before Fajr (at the expense of Tahajjud) or after it (at the expense of reciting the Qur'an) due to childcare, and recalling that "Indeed, the recitation of dawn is ever witnessed"?

The best voluntary act of worship for a mukallaf (accountable individual) is that which is most beneficial for him and his heart, even if it is inherently less virtuous. Combining the virtues of various deeds is better if one is able to do so. Night prayer (Qiyam al-Layl) is the best of supererogatory acts of worship, and it takes precedence over reading the Quran outside of prayer if combining them is not possible, because it is a time-bound act of worship that is missed if its time passes, and it includes reading the Quran and other good deeds. The time-bound morning adhkar (remembrances) take precedence over reading the Quran after Fajr, because they are a time-bound act of worship that is missed if their time passes. The "Quran of Fajr" in His, the Almighty's, saying: (Indeed, the recitation of dawn is ever witnessed) refers to the Fajr prayer, which is witnessed by the angels of the night and day. When it is difficult to combine Qiyam al-Layl with sitting for the remembrance of Allah and reading the Quran after Fajr, Qiyam al-Layl and the morning adhkar take precedence, while maintaining Tahajjud before Fajr and performing the adhkar before sleep after Fajr.