I have a website that has an iframe called on the page that is filled with another website that calls a only-when-viewed-in-an-iframe stylesheet. Would a css file from the main site overwrite styles of the iframe stylesheet for elements in the iframe?
The contents of the <iframe> are like a whole separate browser window. In fact, unless the parent and the <iframe> source come from the exact same domain name, I don't think they can have any interaction at all, as a security precaution.
BTW, I notice your code above has a bug in it. <head> should close before <body> opens. I hope you've got it that way on the live page.