Ok, you've got options here. I think it's kind of hilarious that you immediately jump to cheating on your wife but whatever. That is a whole other issue. I think also that I wasn't properly socialized, because I just don't get the whole fascination that people have with certain positions and how this one or that one is "dirtier" and therefore more fun—to me it's always seemed like if it feels good awesome, if not then who cares.
Thank goodness you told me that your dick isn't small, so that I understand for sure it is your wife's physiology and not yours that is the "problem." Definitely important to establish whose "fault" it is that your generally good sex life is horribly marred by a lack of from-behinding. Fortunately for the both of you, big-assed ladies (and small-to-medium-dicked dudes) have been doing it doggy style since time immemorial. Fucking from behind is all about positioning.
Picture a woman on all fours. Her ass and butthole are facing out, then as you follow the taint around, her pussy is sort underneath, nearer to the axis of her back and belly than facing out with her ass. If you are having trouble getting to the pussy, y'all need to change that angle, bringing her pussy more to the rear. If you're doing this right, the size of her ass shouldn't really matter.
I assume you've experimented with her bowing her back more or opening her legs more. If not, mess around with the angle, or try putting your legs over hers to get your dick closer. There are also positioning aids that you can buy. Remember that not only able-bodied people want to fuck each other—there is a whole world of devices that aid in getting all the parts where you want them and holding them there. The two I would look into in your case are an angled wedge pillow, which your wife could use to support her torso so that she can use her legs to position herself, rather than have to hold her body up, or the doggy sling, which is a kind of swing you hold that goes under her belly, allowing you to adjust the angle better for easier penetration. Both of these items can be found in most internet sex stores.
Good luck with your doggy-style fucking, and I hope it's everything you thought it would be.