Oh dear. These one up-man-ship situations never go well. It's hard to enjoy Thanksgiving dinner, whether you're "competing" or just watching the competitors. I hate feeling like I have to modulate my praise of something on the table that tastes good, or praise something that's 'meh' because I know two women are duking it over over cooking skillz.
I have some seriously competitive cooks in my/DH's family, and my suggestion based on that experience is to NOT try to out-do each other, but rather develop specialties and try to avoid stepping on each others' toes. My SIL makes great pies and appetizers. I don't even try at those things, but I make awesome birthday cakes, cookies, and margaritas. My MIL makes great casseroles and dinner standards. Together we can throw a hell of a multi-course party, and nobody gets bent out of shape.