What have Hester and dimmesdale decided to do about their situation?

Hester and Dimmesdale planned to go back to the "Old World" in England and begin a life together with Pearl, as a family.

It had been determined between them that the Old World, with its crowds and cities, offered them a more eligible shelter and concealment than the wilds of New England or all America, with its alternatives of an Indian wigwam, or the few settlements of Europeans scattered thinly along the sea-board. Not to speak of the clergyman's health, so inadequate to sustain the hardships of a forest life, his native gifts, his culture, and his entire development would secure him a home only in the midst of civilization and refinement; the higher the state the more delicately adapted to it the man. In furtherance of this choice, it so happened that a ship lay in the harbour; one of those unquestionable cruisers, frequent at that day, which, without being absolutely outlaws of the deep, yet roamed over its surface with a remarkable irresponsibility of character. This vessel had recently arrived from the Spanish Main, and within three days' time would sail for Bristol. Hester Prynne--whose vocation, as a self-enlisted Sister of Charity, had brought her acquainted with the captain and crew--could take upon herself to secure the passage of two individuals and a child with all the secrecy which circumstances rendered more than desirable.