Is there sin upon a mother if she prays while her infant is crying?

You bear no sin, Allah willing, for what you did, as a child's crying is not an excuse to delay the prayer beyond its prescribed time. If there is ample time and your daughter is crying due to hunger, you may attend to her needs first and then pray, so that your heart is not preoccupied by her crying, distracting you from devotion. It is permissible for you to carry her during prayer if you are certain of her purity, as the Prophet, peace and blessings be upon him, carried Umamah bint Zaynab during his prayer.