some thoughts. 1- if her children aren’t crying and pulling at her skirts in hunger, she can daven.
2- in a situation as the one described, being supplied with food for a month doesn’t give her any idea where the food will come from in Chesvan or how she will pay the rent, or what to do about her child’s outgrown shoes… There’s enough motivation for prayer even less the worry of hunger for a few weeks. 3- she can go to shul if her kids are fed, as opposed to them not being able to sit in shul, or her needing to spend (part of) her mornings begging or scrounging for food, so there the food would directly contribute to improved tefilla.