Training in a two dog house

Is there any way you can seperate them while working with one?  Confine one to his/her crate with a high value chew toy while you work with the other.

Are both dogs puppies?

Prevention is more the key with a  pup.  If she is tired from exercise before she is allowed any freedom in the house, there will be a lot less of the kind of activity you describe.  Also, don't correct her by saying her name, or "no".  Instead, redirect her by going over to her and issuing a request.  You can use "sit", "leave it", whatever commands she already knows.  If she has gotten an object that you'd rather she didn't, simply "trade" for it by putting a biscuit near her mouth and saying "trade" or "drop".  She will learn the word eventually, which is the object of the exercise.  Until she's out of the second chewing stage, it's best to keep shoes and other stuff out of reach.  As to the trash, put a bit of Vicks Vapo Rub around the rim of the bin - it doesn't exactly smell like food or other good stuff, and most dogs hate the smell and will leave the area alone.
Terriers are willful, but smart - have you tried clicker training?  It's a great way to teach dogs about boundaries, or going to their "place".
www.clickerlessons.com
www.clickertraining.com
www.clickertrainusa.com (free videos)

I have the same problem, I think Trixie thinks Brando is everybody's name, I use it so often. Brando isn't scared of anything Trixie, I think if I ever yelled at Trixie it would just break her heart. So the good thing I don't ever raise my voice now everybody is happier, esp. DH.

If I'm doing an actual training session, I seperate the dogs and just work with one at a time. I'll put one in his crate with something extra awesome and then go to a spot as far in the house as I can from the crated dog, shutting all the doors along the way. Because I use a clicker, if the other dog hears the click, they want to come join in the fun, so I have to do some soundproofing. Working on both at once is a nightmare, especially because they are both at different phases in training and are working on learning different things right now.

Try living in a SIX dog household! []
 
I'll admit that the last few weeks have been out of control with being at the hospital so much and the dogs have been pretty neglected lately.  What I normally do is make sure that everyone gets a few minutes of alone time with me every day.  I do that by either crating with knuckle bones or letting all but one out to play.  I do mini-sessions one on one and when everyone is in, maybe just little short group sessions.  I notice that the less of me that there is to go around, the harder everyone works to get my attention and that makes sessions more difficult.
 
I soooo hope that things continue on the upswing so that I can breath again and give these poor critters the attention they deserve.

I forgot to change something in the OP. I meant to say "working around the dogs", not "with the dogs". When I am doing obedience work, I do separate them, but I am referring to just working around the dogs while I clean the house, do the laundry, etc. I keep Lilly tethered to me with a six foot leash most of the time, unless I'm doing something that I can't have her under-foot. Lexi is 3-4 years old and very well trained around the house, but she needs a refresher course every now and again. My problem is mainly that when Lilly gets into something, I can't scold her without getting Lexi all upset and thinking that I'm scolding her.

We do try to tire out the puppy, but good lord, these terriers are tough! We are starting clicker training (I'm re-reading "Don't shoot the dog" now), which I think will be beneficial for both dogs. Lilly already knows sit and down, about 90% of the time, and we are working on the trade. One of the problems that we have is that now she goes out looking for inappropriate things (namely socks out of the hamper), brings them to me, and waits for a trade. Smart little rascal We are trying to use prevention (she can't get in to trouble if there isn't anything around to get into) but sometimes it seems that the rest of life gets in the way and she gets in to trouble anyway...

Thanks all for the advice!

It's really simple - don't scold Lilly.  Simply give her a command that is incompatible with what she's doing that you don't like.  "Leave it" "Come" can be very useful, and not make your other dog think she's done anything wrong. []