Abused Rescue Dog Pooping on Furniture?

I recently adopted a 1 year old female Aussie/Border Collie mix. She has spent most of her life chained to a tree outside. She is very loving and will let anyone pet her if they sit down next to her, but she is very skittish around everyone, but me. She just recently started peeing and pooping on the sofa if I leave the room and don't let her come with me. She sleeps under my bed and is crate trained. She won't mess in her crate, during the night or even when I'm home. But let me walk out of the room and bam, I have a mess.

I take her for walks, have a fenced-in yard, and let the dogs out frequently throughout the day. I sometimes have to put her leash on her to get her to go outside. We also have a Chihuahua, they mostly just ignore each other, and a 1 year old Aussie rescue I adopted as a puppy. He is fine and they get along great, but I can't have her pooping on my furniture. Any help or training suggestions would be greatly appreciated. Thanks.

By Dawn