Is it permissible to suffice with only the obligatory prayer after sunrise for one who missed the Fajr prayer due to waking up late and caring for children?

Preserving prayer at its appointed time is an obligation, and delaying it until its time expires is a grave sin. Indeed, Allah Almighty has warned those who do so, and it is a greater sin than adultery, theft, and drinking alcohol. The time for Fajr prayer ends at sunrise, and prayer must be prioritized over breastfeeding the two girls unless there is a significant harm. If you do not wake up until after sunrise, there is no blame upon you.