How can a married woman with young children and household responsibilities reconcile her family duties with her acts of worship, such as reading the Quran and performing Qiyam (night prayers), especially during Ramadan, given her feeling of falling short?

You will be rewarded for caring for your daughters, attending to your husband, and managing your household affairs if you intend thereby to seek reward from Allah. All ordinary matters become acts of worship if they are accompanied by the intention of drawing closer to Allah. Continue to care for your family and try to find time to read the Quran and perform supererogatory prayers, even if it's by committing to a fixed daily portion. You can read the Quran and perform adhkar (remembrances) while doing household chores that are not incompatible with them. Balance and moderation in life and giving everyone their due is from the guidance of prophethood. So, fulfill the rights of your Lord first, then the rights of your husband and children, and do not neglect yourself from supererogatory acts and obedience as long as it does not affect the obligatory rights.