introduced a new dog, now both are going to the bathroom in the house at all times

Question
We got a sheltered dog from a county shelter.  His name is Lucky, a Jack Russel Terrior mix (not sure what hes mixed with, just looks like a slighty bigger jack russell) and he knew from the start to go to the bathroom when we took him for walks and he'd do it right away, always.  

Never had a problem with him, even when I started my new job and my fiancee and I were both working the same days.  He would be left in our apartment, alone for about 6 hours at most.  We both work at the same store and they usally have me start before the store opens and she starts when it opens or later so even if we both work full time shifts he is alone 6 hours at most including drive time.

We had him for a little over two weeks and thought we should get him a friend to play with when we are not home.  He was never very distructive when we did leave him alone except for a few minor incidents.  

We got Buddy, he's around 1 years old as well, he's a Chihuahua mix (we're almost positive he's mixed with a jack russell, he looks just like one except for his face and he's got more brown then white on him) and he was very scared when we brought him home, more so then lucky.  He was getting a feel for the place and peed on some towels in the bathroom, my fiancee and I were both easy on him since he just came from the shelter and was so scared.

Well he continued to do it and it upset us, well now he's doing it still, anywhere, even on the bed while we were sleeping last night causing us to change the sheets and everything at 2:30 in the morning.  Now Lucky is picking up on it and doing the same thing and he knows better!!  

We have been leaving the door open to your small deck hoping they'll go to the bath room out there while we're gone if they have to and for the most part they have and I came home from work today while my fiancee was still at work and was glad to see they didn't pee in the house, was just about to take them out side and saw poo on the carpet, the real nasty kind.  

I was very upset!  

I believe it was lucky because when i took them out after i cleaned it up and cleaned the deck up lucky had the same type of runny poo.

What can we do to provent them from doing this inside the house when they do it while we're home in a different room, while we're sleeping, and while we're gone!

We dont want to crate them becuase we want them to play together and they have been getting along great after only a couple of days.

What can we do?  It's when we are home, and gone, and sleeping.  We really did not want to get angry at them since when we come home we are not 100% sure who it was that did it and they could of done it right after we left and might have forgot all about it when we get home and not understand what we are upset about.

Also, Buddy, my new dog has been adjusting better but slowly.  He rarely goes potty outside.  Only once was he energized and running next to Lucky.  Usually he walks so and behind us, stops often when he hears a sound or a noise and gets scared of people and animals.  How can i get him to go to the bathroom outside?

A problem is we are gone for a good amount of hours every day (except we both have this tuesday off, i am taking wednesday off, she has thursday off, and I have friday off).  We really do not want to give buddy back to the shelter since we hate to see those poor guys in there but we also can't go on with them doing there thing anywhere in the house they want, including the bed where they sleep every night, etc.

Answer
If you are only gone six hours, I would suggest you crate them for now until you have things under control.  Crate them next to each other and they will still have company.
second:  if one of them has a loose stool, that has to be gotten under control before he can be rehousebroken.  You can't expect a sick dog to be able to control himself under those conditions.
third on Tuesday, make sure you keep them with you, on  a leash even inthe house.  the dog that is urinating on you in bed is claiming territory, so you may want to be sterner with him.  Either crate him at night, until he learns or do not let him on the bed and confine him to an area that he will not ruin.   Lucky is just copying him to maintain his territory because the new dog is trying to claim the territory as his.  I would crate all and start from scratch.  This doesn't just happen with dogs, it happens with children too.  A potty trained child will start to wet his pants when a new baby is brought into the house.   
Let me know how all this works, give Lucky the praise for going outside and make sure Buddy is confined until he is house broken, or you will have two unhousebroken dogs.
good luck
nancy