Is stuttering hereditary?

Stuttering can run in families, but no one knows its cause. Most children do go through a phase of stuttering and grow out of it on their own. The example you gave showed her interjecting "um" into her sentence. This may or may not be a sign of stuttering. Does she repeat parts of words (i.e. c-c-cat or bi-bi-bike)? Does she prolong sounds in words (i.e. mmmmmom)? Does she show tension in her neck and face when she speaks? If she does these things, you may want grandma to call the local school district where they can do a free essment and can provide free speech therapy. Early intervention is a good idea. But, again, most kids go through phases. My 2 year old was just doing it a few weeks ago and has now stopped. My 4 year old has now started. I'm not worried about them.