Why would she not accept his child if the child actually was his. I think Adele has strict rules for herself. Anyway, it is good that Adele realized her mistake, and it didn't take too long for her to understand there was a mistake. And Edward was very understanding and kind that he wanted to go back to Adele. Fate brought them together again.
Yes, she is stubborn and knowing she didn't tell him about having a child some days to their wedding isn't that nice. She learned the hard way, but it is nice Edward still wants her.