My daughter (11), wife, and mother in-law all have extremely similar handwriting.
Why is this? Is handwriting a inheritable trait?
Your discussing the cog sci called graphology. It doesn't really work in general cases but its a nice idea. I would say its a happy accident that they look alike. My letter R look like my father's R because I wanted to please him at that age so I mimicked his handwriting.
Graphology is the study of handwriting. As a theory or practice for inferring a person's character, disposition, and attitudes from their handwriting, graphology is generally considered pseudoscience.
Graphology has been controversial for more than a century. Although supporters point to the anecdotal evidence of thousands of positive testimonials as a reason to use it for personality evaluation, most empirical studies fail to show the validity claimed by its supporters.
Thing is, when we look at something for a while, it influences us to, in some ways, follow it. If I am not mistaken, a similar principle works for yawning and how a person can yawn just by looking at someone else who does. I wish to elucidate with a personal experience. In my high school, there was this girl with amazing handwriting. I got down with the pox so I used her notes to study. And soon, I realized I have started writing a bit like her. My letter were slightly tilted (hers was at a precise 80 degrees and was consistent across the page) and more cursive. My work became more neat like hers and far more presentable. And I wasn't making a conscious effort to mimic her handwriting at all. It just happens.
This might help to explain what I am trying to say a bit better, although it is not about writing, I think it can be extrapolated: http://www.youtube.com/watch?v=4NpG4F9yq00
I don't know of any particular research that's looked at this, but based on general principles, I'd conjecture: