Perhaps the best way to support the decision to steal food is to use utilitarian philosophy. Utilitarianism holds that people should act in ways that bring the greatest amount of happiness to the greatest number of people. Put differently, when faced with a problem, you have to ask which course of action would do more to increase overall happiness in your society or your community.
From this point of view, Mary should steal. The amount of happiness that she and her children would gain would be quite large indeed. Her children would stop being hungry and she would no longer have to suffer emotionally because of their hunger. In addition, there is very little unhappiness that will result from her theft. Presumably the grocery store from which she steals will not be hurt a great deal by her theft. The harm to it will surely be less than the benefit to her.
In this way, you can use utilitarianism to justify theft in this case.