Top Dog?

So, yesterday I took Mia to work with me. She loves going for car rides, is well behaved around other people and in new places, and could use a break from the abuse Wiggles heaps on her all day, every day in an attempt to be the "bigger" dog. Seemed win/win, you know.
I failed to understand the fine line my pups are balancing with regards to their relevant positions in our little world. When Mia and I returned home last night, Wiggles increased her posturing and aggressive behavior. I tried all the tricks I've used in the past: leash work, training sessions, socialization-type things, etc. Things seemed edgy, but better when it came time to put them to bed. Per the usual, Mia and Trooper were in the igloo, and Wiggles was on the blanket (tucked under another blanket cuz the people in our house can't help projecting and anthropomorphizing their pets).
This morning I woke up to the sound of a dog yelping in a most unhappy way. I rushed outside to release them, sure that Wiggles had somehow hurt Mia with her obnoxious one-up-man-ship. I looked her all over, and almost missed the gaping wound on Wiggles' ear. It looks pretty ugly. Blood on the inside and outside make me think someone bit right through it. I've made an appointment to have the vet look at it. Everyone seems to be getting along okay now, although Mia is acting pretty spooked.
We're going to get a second igloo as soon as possible. (We have a second doghouse already, but it's second hand and none of the dogs will go inside it.) Other than that and not ever taking Mia somewhere without Wiggles again, I have no idea how to help them work this out. All I know is that I am tired of dealing with it.

UPDATE:
I swear our vet thinks we're idiots.
.....
As he began to examine Wiggles, he looked inside her ear.
"Is this the injury?" He points to the miniscule wound you can see from that side. I can tell he is wondering why the hell we bothered him with this injury he can barely see. I lean in.
"Yes, that's part of it. But I'm more worried about..."
As I am speaking he turns the ear over and notices the inch long chunk of fur and skin missing.
"Oh! This is definitely going to need sutures," he says to his assistant as if one of us had disagreed with him. I bite my tongue to stop myself from making some inappropriate, albeit probably very witty, remark.
.....
We ended up signing the anesthesia forms and leaving her to have her ear stitched up. Poor baby is going to be be all wobbly instead of wiggly when we pick her up at 4:00.