Aggressively Peanut

First, I noticed you are constantly applying human emotions to the dogs (jealousy, frustration, domineering, insecurity, resentful, etc).  I would not look at it that way.

Second, I guess in general with incidents like these, I would start with more management.  The offending dog needs to be restricted from the dogs she is going after and the resources she's trying to guard.  She should not be allowed to bully other dogs such that they "shivering scared".  Don't try to rationalize why it happens or project emotions onto the dog's behavior (goes with the above).  Examine what happens when and brainstorm how you can STOP it from being allowed.  For example, if Peanut goes after other dogs while Martha is around, then confine Peanut to a crate, behind a gate, or in another room while Martha is interacting with the other dogs. If Peanut cannot be nice and under control during a certain activity, then she looses the privilege of that activity until you've done the necessary behavior modification.

Third, I would start a strict "NILIF" program (Google that, plenty of good info already out there). 

Others will likely suggest a full vet workup to rule out any medical causes like pain or thyroid issues.

  I suggest you consult a qualified, experienced behaviorist for an in home visit.   

Burl

With no consistent place or trigger event

There is a consistent trigger and that appears to be resource guarding something of value.  This could become much more serious and I wouldn't rely on internet advice alone for help.  

She did just get a vet checkup, and her beagle ear flappers do cause her to be prone to lots of ear infections requiring ear drops. She is getting over a mild infection now.

99.99% of the time, we are a happy laid-back pack of 5. I was wondering if the infrequency of her outbursts is such that it would be considered not that uncommon or intolerable? Of course, we want it stopped.

Burl

 

99.99% of the time, we are a happy laid-back pack of 5. I was wondering if the infrequency of her outbursts is such that it would be considered not that uncommon or intolerable?

Maybe, but what if it only continues to escalate?  Then you'd look back and wonder why you didn't nip it in the bud when it was still possible to intervene.

I have a pack of large dogs - a female German shepherd, a large male mix, and a male German shepherd (intact) and sometimes have a puppy (intact) and have no such squabbles.  Every dog started out being confined and following a pretty strict, predictable routine and slowly earned their freedoms and privileges and variations to the routine.  Any sort of resource guarding behavior would result in an instant revoking of privilege (for example, if a dog growled or snarked at another dog on the bed, that dog is immediately removed and no longer allowed on the bed).  To be honest I've never had to revoke privileges, but I certainly would if there were any incidents like you describe.  Again I would not worry about why you think the dog is doing it ("my second request must have frustrated her wish for me to get up to get their breakfast";) and just don't let it happen again.

It seems the same as NILIF. As for Peanut, about the only 'trick' she has is to sit for food - but I wonder if she thinks she (not me) is producing food when she sits!

Burl

What do you all think of Dr. Coren's 'Work For a Living' idea

It's the same principal as NILIF.  The key is consistency, IMO.  As Dr. Coren mentions, all members of the family should be on the same page.

 I'm glad dogs don't worry about theories and semantics, the way humans do.  They do what works to get them what they want/need.  It's a ridiculously easy principle.  Being the so called smarter species, we tend to make things more complicated than necessary sometimes. 

Burl

As for Peanut, about the only 'trick' she has is to sit for food - but I wonder if she thinks she (not me) is producing food when she sits!

I doubt it.    But if you see her looking around for food when she randomly sits, you could be on to something. lol

What is the best way to split up the scuffle (what type of noise)? If splitting them causes the blood, is it better to let them finish themselves?

Burl

I was looking in the behavioral problems subforum here http://forum.dog.com/forums/t/107164.aspx where spiritdogs said "A scuffle is a scuffle and is easily broken up with noise. When you have to physically break up two dogs (which is how most redirected bites happen), and one goes running back for the other as if to kill, that is not ok in a pet home IMO. You should not live in fear, and neither should T-Bone. "

 

What is the best way to split up the scuffle (what type of noise)? If splitting them causes the blood, is it better to let them finish themselves?

I don't think this is something you should try to manage without help.  Take Jackie's original suggestion and find a qualified behaviorist to help.  Sometimes, the dog you think is the aggressor isn't, and sometimes you miss signals that are important not to miss.  NILIF is training, this requires behavior modification or management.  Not that training is bad - the more control you have over your dogs, the better (notice I did not say anything about dominance).  Dogs that have an occasional scuffle with no blood is normal behavior.  Dogs that continually repeat this behavior, to the point of bullying other dogs, or that do injure one another or injure humans are not OK and need help from someone who knows what they are doing.  Animal Behavior Society or IAABC have listings of behavior professionals.