K.V.
Hi R.. I am a speech therapist. While I cannot diagnose whether your niece has a real problem with stuttering without evaluating her, I can tell you that it is not unusual for preschool children to go through a period of some stuttering. Stressful situations can significantly increase stuttering so it is not a shock that this would happen with big changes in the household. Here is a link to the ASHA (American Speech and Hearing Assoc)website that explains about stuttering.
http://www.asha.org/public/speech/disorders/stuttering.htm
I hope this helps!
K.