Your child has seen a lot and probably suffered emotionally too by this tender age.Shes 13 and would be experiencing puberty which brings in its own mood swings ,hormonal changes and is a challenging time for a child.
Her mother left her when she was young ,her attachment style ,her trust in the world would have shaken ,now she has a new mother .All these are a lot of changes or a young child to deal with , she might have a lot of apprehensions which she might not be able to say to you and her insecurities could be presenting themselves in the form of stammering.Stammering basically indicates her anxiety, nervousness.Please see a child Psychologist or a family therapist .
Next Steps
please consult me ,this needs very delicate handling
Health Tips
please try to see the world from your child's view ,do not scold her for her stammering .Let her be relaxed,try to make the atmosphere jovial at home