Balancing on the wire separating "culture" and "stereotype"

As many of you know, this course evolved from much of the reading I did when I was first drafting my novel, Borrowed Horses.  The main character of the novel, Joannie Edson, is a white woman living in Idaho, and her love interest is Timothy, the son of a Welsh father and Spokane mother.  Because I've long been an admirer of Alexie's work, it was impossible for me to write without his poem, "How to Write the Great American Indian Novel" in my mind, and I still read it, thinking of my own book, and wondering if I've been careful enough to create a character that feels real and whole and that represents some of this rich culture without seeming stereotyped.

This is a devilish hard line to walk.  I'll give an example from my own culture to illustrate--

When shopping for houses, we stumbled upon one that might have been nice if its previous owner hadn't chosen to cover all the walls of one room with plastic wood laminate paneling (gag).  Someone who I will not identify here jokingly commented that the previous owners must have been Irish because the Irish love fake wood paneling.  "Hey!" I yelled, wanting to launch a protest in defense of my mother's people, but then I remembered my grandmother and grandfather, who pulled down the solid mahogany wainscoting in their turn of the century semi-detached in Philly and replaced it with (cringe) fake wood paneling.  And then I thought of one uncle's home, and another.  Paneling, paneling, paneling.

So, would I have been right to call this person out for a stereotype, or had s/he simply located an aspect of the culture?  (Immigrant practicality?  Too much time spent scrubbing the darned wood in other, wealthier people's homes?)  If I wrote about a character who was born of Irish immigrants, would placing paneling on the walls of her childhood home be stereotyping or merely a nod to a cultural phenomenon? 

To get back to my own novel, if Timothy has a dream (as he, like Joannie, does), then am I giving him a vision and violating my own desire to avoid stereotyping?  And are then Joannie's dreams, the white girl who, according to Alexie's satiric poem, is "Indian by proximity" [line 27] affected by this, too?  Do I remove the dreams?  But, then, don't people have dreams?  And aren't those dreams sometimes oddly telling of the knowledge that we carry subconsciously?  And does it matter that some of the dreams were written before the character Timothy was introduced to the novel?

I am not so naive a writer as to believe that, just because some of the sections predate Timothy's creation, that his presence won't affect how they're read, and much of my revision has been dedicated to the task of separating him as far from stereotype as possible and creating a character that readers will sympathize with and admire.  Still, I read my own work with Alexie very much in mind.  I want him to approve.