I don't know if this would be considered "separation anxiety" or just plain jealousy over another dog?

A little background:
I am the only one who works Misha or Chaos; classes, walks etc. Classes have always been taken with just one or the other; walks we all three do together (me walking in between the dogs on leashes). Misha is 3 1/2, and has been a "velcro" dog from puppyhood. Chaos is 17 months, and is not as "velcro-y" as Misha (likes to be in the same room, but does not need to see me all the time).

I started a new class; it is a "proof for distractions" and a "get ready for Obedience Trial" type - very relaxed with 6 dogs. My trainer is letting me bring both dogs. The beginning of the 1st class, I put Chaos in a wire pen and worked with Misha for the 1st 1/2 hour, then changed dogs. This is where the problem started - Misha started throwing a fit! crying, whinning, yipping. I told her "quiet" - she ignored me. After about 5 minutes of ignoring her, she finally subsided to just a continuing whine (with a few yips thrown in for good measure) and pacing/panting.

When I took her out of the pen (after a 1/2 hour) she was panting and agitated, and wanted to jump and bark at Chaos (I corrected this behavior with a leash pop). When we got home, all she wanted to do was lay on the couch next to me.

2nd class; I worked Chaos 1st - same behavior from Misha. When I changed dogs, it took a good 20 minutes for Misha to jack down enough to pay attention to me to get anything out of her.

My question is, do you think this behavior will get better? Did I "traumatize" her? Any suggestions on how to help her to get calmer while seeing me work another dog?

I don't think you "traumatized" her.

When we work with our dogs in the winter, we have an area seet up in the basement for their crates and for them to be trained. 2 of the 3 will be crated while the one is trained (only obedience stuff), and my GSD girl gets a little excited in her crate, like she wants out really bad. Same thing with my Lab. I don't know what to tell you-cause to me it's kind of normal and I ignore it.

Having to redirect an excited dog-in your case Misha-can be no easy task. Are you allowed to bring in toys or anything that she loves to play with (I don't know what the class rules are)? If so, try and use a favorite toy(orbee, etc.) to get her redirected and paying attention to you.

You did not traumatize her. Simple possessiveness is what you're seeing, IMO. I would ignore her completely unless she is ANGELIC in that pen at class. She only gets her turn if she behaves and waits patiently; otherwise, she sits in a crate while Chaos has all the fun. JMO.

or--you could try just covering the crate while you work the other dog. save unnecessary stress on everyone.

Do you have dog crates at home?

If so, how does Misha act when she is crated and the other dog is loose?

If that never happens, time to get two dog crates and practice! Get the dogs used to being separate, and having YOU choose who gets to be out. As jenni said, Misha can only come out when she is quiet and behaved. (Make sure you praise her when she is quiet before you let her out, so she knows exactly what is expected). If you let her out then praise her, she will think you are praising her for something she did after you let her out (like get excited).

Until you have trained her, at home, to be QUIET until it is her turn, leave her crated in the car (unless it is too cold), so other people don't have to listen to her the whole time.

Does Misha also have separation anxiety? How is she when you leave the house without her?

We only have 1 crate at home; Misha had "graduated" out of it before I got Chaos. So, no - she has not watched me work him before.

Misha has always been okay when I leave her at home; she does get "upset" when I leave her home with my husband and take Chaos to class - but settles down once we are gone.

Thank you for these suggestions - I think I will be practicing OB with Chaos while Misha is in the crate at home. Her actions at class really surprised me; I thought she would be fine since she could see me, and had been to the training facility alot.

...after re-reading this, I am wondering WHY I didn't do this in the first place??! (practice at home 1st). So, thank you for taking the time to reply to a kinda dumb question...