First thought is that your wife sounds selfish, esp. over being critical of what the kids have given/produced.
However - my second thought is that perhaps you, personally need to be rather more competent. A father of six DC really shouldn't be a 'crap cook' whose attempt at a simple meal is 'a failure'. I do most of the cooking, and never have a meal cooked for me on my birthday, and I do find that irritating (though I don't show it). Did you wrap your presents nicely, pick a card with a meaningful picture and give them to her in a nice, festive way (not shoving them over unwrapped with a mumble about not having time)?
When my DC make a cake for my DH, I supervise it, so that it's edible (not sure the ages of your DC, mine are young). My DH never makes a cake for me, nor buys one - I buy my own, which I find annoying as well.
The biggest thing I find annoying though is for him to have a kind of hangdog approach to my birthday - a kind of 'i know this isn't really good enough' attitude, which then requires me to be upbeat and all 'oh, it's lovely' in order for it to be a nice day.
I don't want parties or expensive gifts. But I do want a nice cheerful atmosphere (that I don't have to create), with wrapped gifts, a card, a cake, and a meal I don't have to cook/shop for/book a table for/think about. And I want DH to provide the necessary help that the DC need to contribute their part to all this (because it makes them happy and competent to do so)