So, the Beloved and I have two dogs: a four year old basenji bitch*, and a six month old dachshund (male).
More times than I can count, I’ve had to go pull them apart for fighting over who can get closer to the Beloved on the chesterfield or on the bed. Almost always, it’s the basenji being extremely aggresive to keep the little guy from getting closer to the Beloved than the basenji is. That part I can follow in dog-thought - we’ve had the basenji since she was a puppy, and being close to the alphas is a sign of pack hierarchy, etc., so she wants to keep the little guy from squeezing her out.
But, they don’t fight like that to get close to me. They’re generally quite content to snuggle up, one on each side, or even both on the same side. The basenji only gets a bit owly if the little guy starts intruding on her personal space, but doesn’t seem bothered by him getting close to me.
So, does that mean the Beloved is the queen of the pack and I’m just dog food, or what? 
You’ve kind of answered your own question. The dogs view Mrs. Piper as alpha, and you’re beta, and therefore, you’re not nearly important enough to fight over.
This is probably due to some aspect of interaction with the dogs that differs between the Mrs. and you – does she always (or more often than not) feed them, walk them or have some special ritual or activity that only she does with them? If so, the dogs have attached significance to that particular difference between you and have put her, therefore, further up on the pack hierarchy.
The fighting is rough, and should be addressed. But someone’s got to be the alpha, and it’s really too late to change the pack order status in the household, so that aspect of things issomething that you’re going to have to live with, I’d think.
I’ve had something similar happen, and figured since I only worked 8 hours as opposed to my SO’s twelve, I spent a lot more time with our dog. Sometimes during play, my SO would tug-o-war with our dog or maybe go up behind him and give his tail a playful pull and pretend he hadn’t. When the dog looked at me, I’d say, “go get him,” or “don’t let him do that to you,” etc. It was a huge game, ending in giggles from humans and cuddles from the dog. One day, the roles were reversed and when the SO told our dog to, “go get her,” it provided for quite a different response. Our dog stopped, looked at me then the SO, and went after the SO anyway! heh Turns out, he never would “go after” me, even in play.
All of that to say, I think TeaElle’s answer makes a lot of sense.
