Regina would never have left anything open–she is smart to know to cover her tracks well. She probably got to Belle after the events of Dreamy. Either she took Belle after that episode, or she convinced her father to give her custody–I don’t think her father is a cruel man, but he could easily be tricked. Regina could have told him that Rumpelstiltskin tainted Belle’s mind and that she needed to be treated. Then maybe tell her father and the whole kingdom that the treatment went bad and Belle killed herself out of grief.