Oh my how awful for all of you! I am so sorry for your loss of the one dog.
For the 5 year old, she has had extreme trauma, and needs time, patience, and desensitizing to overcome this. You may want to phone a trainer for advise.
I suggest you start slowly, use plenty of treats. Walk around inside the house with her, on leash, perhaps. As you and she approach that door to the back yard, treat and praise, celebrate! Do this 3 or 4 times not more than that, then let her off leash, training session over. Do this a few times daily for a week.
As with any desensitizing exercise, you have to progress slowly. The next step may be having her closer to the door, or perhaps having the door open. Again do this multiple times daily, lots of treats and praise, don't force her to do more than she is ready to handle.
Any adults, even teens in the house, can take a turn during the day working with her on the exercise.
I don't know what is immediately outside that back door, a landing area, steps, but take it one 'step' at a time. Get her out on the landing, treats and praise and let her get right back in to the house.
While you are working on this, step by step, try walking her on a regular schedule. Most dogs poop twice a day. If you feed her about the same amount at about the same time daily, you should be able to figure out when she has to poop, and set up walkies for that time.
Work on a separate project while out on walkies. See, you have to break each bit down into small increments, bits which she can handle, and then slowly build on that base. As a car approaches, have her sit and face you, and give her lots of treats and praise. Resume walkies after the car / truck has passed by. See how she fairs best, with her sittting back to the road (maybe not) or facing you with the road behind YOU so she can see the car go past. Try it out and see which has her less nervous to start.
It will take time, perhaps 3 or 4 months. But she is 5 years, you have lots of life together still, and you can work this through and help her over this so she can enjoy life in her home again.
When she goes in the house, don't reprimand her for now. IMO that is just making things worse, getting her more nervous. Since she seems to prefer the parlour, consider this. I don't know if that room is carpet or hardwoods, if it is a room you and family use regularly or what. Can you set down tarps to cover that floor / carpet and protect it, then put out either pee pads or newspapers, for easier clean up. In time, when she is comfortable in her own back yard again, you will want to set the pee pads or newspaper out there for a time to encourage her to 'go' out there again. See, don't expect that she resumes her duties out there just because she is comfortable out there. Take it slowly step by step. Some she will work through quickly and it may be that by the end, this step will just fall into place.
Prior to when I adopted my Sugar (now at Rainbow Bridge) she had been attacked by a bull mastiff, picked up by the head and shaken. At the time, Sugar was blind with age related cataracts so she never saw the the dog coming. Once she was in my home, I lined her up for cataract surgery to regain her sight. But that was not enough. Every time she heard another dog, she was in extreme panic and took off. I could be walking her on leash around the neighborhood, the dog could be a small chihuahua barking next street over at the mail carrier, and Sugar was terrified. Once she even slipped her collar and took off! Luckily, she darted to my home (she'd been living here about 2 weeks and had not had the surgery yet so was still blind at this point!) and someone at home let her in. It took lots of training time and treats, but 4 months after the surgery she finally was calmer when she heard or saw another dog near us.
Good luck and do let us know how things progress!
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