She felt her cheek pale and cold and, out of a maze of distress, she prayed to God to direct her, to show her what was her duty. What does it mean?
Eveline's mother is no longer alive. Eveline has become the woman of the house, essentially assuming all the responsibilities of her late mother. She feels a duty to uphold and continue those responsibilities. Eveline recalls her promise to her mother to "keep the home together" as long as she can. Eveline longs to escape, so, Eveline is torn between the promise to her mother to stay and keep the family together and the desire to escape.
Thus, she is in a "maze of distress" because she can not make up her mind. She feels "pale and cold" She prays to God for some guidance on the question: should she stay with her father or should she go with Frank. If she is trying to see what her duty is, that means that she questions whether she should be loyal to father (via the promise to her mother) or if she should be loyal to her self, to pursue her own goals in life. In the end, perhaps out of guilt, she can not leave.