I just rescued a three-year-old dog. I use the crate to as a den for her where she hangs out with toys and treats. She also eats her meals in there. The door is often left open for her to practice going in and out on her own. Lately, she is going inside to pee with door open and when she is confined for short periods. I clean thoroughly afterwards. I have a backyard where she is being taught to potty. Further, she will not pee or poop on the walks while my other dog does like clockwork. I am so confused since she is not put in there for punishment. Also, if she sees a blanket or doggie bed in another part of the house she pees on it.

Most likley territorial, I am assuming you rescued from a shelter? And I would assume that they did a vet check?
See one of the things about rescue dogs is that most times no one knows what their history is like. She could have been kept in a pen all the time and forced to use the potty there. It will take some time to help her adjust to the new rules and regulations of our home. While it's a good idea to feed, and use her kennel as a den, why not trying to only use it for when you are going out or going to bed.
Maybe longer time outside could help her, or more excersise when you guys are out side. She may be thrown off my the other dogs presence and it may be intimidating for her to use the potty with company, probably not the case, but could be an issue for her.

Thank you for your response. My dog came from the SPCA and had several vet checks. I just moved her crate to another room and put another dog bed down for her to use in case she has territorial issues. Shortly after, she went outside but did not pee. Immediately after she went into the new bed, she fussed with the clean blanket, as she does, and peed on it! We went outside, then she came back and got into my other dogs bed with him. I am lost. Every time I wash a blanket she pees on it. I am trying to make it as cozy as possible.

My little black poodle Prada will poop on anything you leave laying on the floor, if there is a jacket or a cushion on the floor she will poop on it.

She only does this if we leave her alone for a long period and I'm guessing she just can't hold it anymore.
She is trying to be clean.
She knows that pooping on the floor is bad from what we have taught her so she tries to poop on something! It's a pain when you have floorboards that would be much easier to clean up ;)

She hasn't done this for quite a few months now, now when we go out I make sure she stays outside for a long timebefore we go out. I walk around the backyard with her or even just sit out there with her until she goes.

It could be a scent thing as well, with the pillow with the other dog, she is smelling the other dog on it, when you are buying or washing her new balnkets, it could be the smell of other people or the detergent.
It just sounds to me that she doesn't know that her job is to potty out side. Did the SPCA say anything about if she were potty trained?
What's the breed and age?

This doesn't sound territorial to me. It sounds like a housebreaking issue. The tried and true method is to take her outside and stay there until she goes. When she does, lavish attention and treats on her. Inside, if she starts to go on something, take her out immediately and take the item up, clean it and put the same item back where it's supposed to go. It's very helpful to have two people working this, so that she can be interrupted and taken outside and the item cleaned at the same time.

Feral dogs try to hide their scent if there are other predators in the area, especially if they've given birth. Is she old enough to have had a litter?

That's kind of what I was trying to get at, just didn't come out so clear :S
I was wondering that because of the fact that the dog doesn't go on the other dogs pillow, just on her new or freshly cleaned one?
I agree, I think it is a housebreaking issue. Was she just spayed when she went to the SPCA, do you know how long she has been spayed for?

Thanks for the advice. My dog is a girl, she was spayed on 11-17-09 at SPCA, before that she was a stray picked up from Animal Control so her history is unknown. Her estimated age is three, she is part Chihuahua. The other part appears to be greyhound, maybe italian greyhound due to her size and boy can she run! That is only my guess.

Since she has had her own bed she does not go in it, she still shares with the other one.