Is what the questioner did towards her friend by getting engaged to her former fiancé considered betrayal, and is it permissible for her to visit the graves of her daughters whom she miscarried?

Breaking off an engagement without a legitimate Shar'i (Islamic legal) excuse is a blameworthy breaking of a promise. Accepting a marriage proposal from a man who previously proposed to your friend is not betrayal, as long as his previous engagement was dissolved; there is no harm in that. Marrying a man who is already married or accepting his proposal is not considered betrayal, for a man is permitted to combine up to four wives. Artificial insemination has permissible and prohibited cases. Intentional abortion of a fetus is not permissible except in cases of recognized legitimate harm or fear for the mother's life. There is no need to grieve or worry about not visiting stillborn infants in the hospital; what is required is to bury them immediately, and visiting graves is permissible under certain conditions.