In the state of Rhode Island the well being of the child is the primary consideration of the courts in determining child custody. It is also called the "best interests of the child." Now, Rhode Island is a no fault state so arguably a "fault" ground such as adultery should not be considered here. If you have started divorce proceeding then the court views that as a date certain that the marriage can be deemed irreparably damaged and so your new relationship may not come in to play. But make sure that thigs are above board for the kids sake anyway. Good luck.