Is a mother's prayer considered unacceptable if her child disturbs her during the prayer, and is it better to delay the prayer to avoid this, even if it leads to its time expiring and performing it as a makeup (qada')?

A Muslim must perform the prayer at its appointed time, for "indeed, prayer has been decreed upon the believers a book [i.e., obligation] of fixed times." It is not permissible to delay the prayer beyond its time except for an excuse. So, if a Muslim does not find water, he should perform tayammum (dry ablution) and pray, even if he knows that water will become available after the time for the prayer has expired. The passing of a child in front of his mother while she is praying or her carrying him during the prayer does not invalidate the prayer. The Prophet, peace and blessings be upon him, carried Umamah bint Zaynab while he was praying, and Al-Hasan or Al-Husayn rode on his back while he was prostrating.